The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / / Masahico Saito, Daniel E. Flath, J. Scott Carter.
Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2021] ©1996 |
Year of Publication: | 2021 |
Language: | English |
Series: | Mathematical Notes ;
109 |
Online Access: | |
Physical Description: | 1 online resource (176 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9780691234670 |
---|---|
ctrlnum |
(DE-B1597)589790 |
collection |
bib_alma |
record_format |
marc |
spelling |
Carter, J. Scott, author. aut http://id.loc.gov/vocabulary/relators/aut The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / Masahico Saito, Daniel E. Flath, J. Scott Carter. Princeton, NJ : Princeton University Press, [2021] ©1996 1 online resource (176 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Notes ; 109 Frontmatter -- Contents -- Foreword -- 1 Introduction -- 2 Representations of U(sl(2)) -- 3 Quantum sl(2) -- 4 The Quantum Trace and Color Representations -- 5 The Turaev-Viro Invariant -- References restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals. The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Quantum groups. Representations of groups. MATHEMATICS / Algebra / Abstract. bisacsh Flath, Daniel E., author. aut http://id.loc.gov/vocabulary/relators/aut Saito, Masahico, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 https://doi.org/10.1515/9780691234670?locatt=mode:legacy https://www.degruyter.com/isbn/9780691234670 Cover https://www.degruyter.com/cover/covers/9780691234670.jpg |
language |
English |
format |
eBook |
author |
Carter, J. Scott, Carter, J. Scott, Flath, Daniel E., Saito, Masahico, |
spellingShingle |
Carter, J. Scott, Carter, J. Scott, Flath, Daniel E., Saito, Masahico, The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / Mathematical Notes ; Frontmatter -- Contents -- Foreword -- 1 Introduction -- 2 Representations of U(sl(2)) -- 3 Quantum sl(2) -- 4 The Quantum Trace and Color Representations -- 5 The Turaev-Viro Invariant -- References |
author_facet |
Carter, J. Scott, Carter, J. Scott, Flath, Daniel E., Saito, Masahico, Flath, Daniel E., Flath, Daniel E., Saito, Masahico, Saito, Masahico, |
author_variant |
j s c js jsc j s c js jsc d e f de def m s ms |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Flath, Daniel E., Flath, Daniel E., Saito, Masahico, Saito, Masahico, |
author2_variant |
d e f de def m s ms |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Carter, J. Scott, |
title |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / |
title_full |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / Masahico Saito, Daniel E. Flath, J. Scott Carter. |
title_fullStr |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / Masahico Saito, Daniel E. Flath, J. Scott Carter. |
title_full_unstemmed |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / Masahico Saito, Daniel E. Flath, J. Scott Carter. |
title_auth |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / |
title_alt |
Frontmatter -- Contents -- Foreword -- 1 Introduction -- 2 Representations of U(sl(2)) -- 3 Quantum sl(2) -- 4 The Quantum Trace and Color Representations -- 5 The Turaev-Viro Invariant -- References |
title_new |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / |
title_sort |
the classical and quantum 6j-symbols. (mn-43), volume 43 / |
series |
Mathematical Notes ; |
series2 |
Mathematical Notes ; |
publisher |
Princeton University Press, |
publishDate |
2021 |
physical |
1 online resource (176 p.) |
contents |
Frontmatter -- Contents -- Foreword -- 1 Introduction -- 2 Representations of U(sl(2)) -- 3 Quantum sl(2) -- 4 The Quantum Trace and Color Representations -- 5 The Turaev-Viro Invariant -- References |
isbn |
9780691234670 9783110442496 |
callnumber-first |
Q - Science |
callnumber-subject |
QC - Physics |
callnumber-label |
QC174 |
callnumber-sort |
QC 3174.17 G7 C37 41995EB |
url |
https://doi.org/10.1515/9780691234670?locatt=mode:legacy https://www.degruyter.com/isbn/9780691234670 https://www.degruyter.com/cover/covers/9780691234670.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
530 - Physics |
dewey-ones |
530 - Physics |
dewey-full |
530.1/2/0151255 |
dewey-sort |
3530.1 12 6151255 |
dewey-raw |
530.1/2/0151255 |
dewey-search |
530.1/2/0151255 |
doi_str_mv |
10.1515/9780691234670?locatt=mode:legacy |
work_keys_str_mv |
AT carterjscott theclassicalandquantum6jsymbolsmn43volume43 AT flathdaniele theclassicalandquantum6jsymbolsmn43volume43 AT saitomasahico theclassicalandquantum6jsymbolsmn43volume43 AT carterjscott classicalandquantum6jsymbolsmn43volume43 AT flathdaniele classicalandquantum6jsymbolsmn43volume43 AT saitomasahico classicalandquantum6jsymbolsmn43volume43 |
status_str |
n |
ids_txt_mv |
(DE-B1597)589790 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
The Classical and Quantum 6j-symbols. (MN-43), Volume 43 / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
author2_original_writing_str_mv |
noLinkedField noLinkedField noLinkedField noLinkedField |
_version_ |
1806143298907144192 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04469nam a22006855i 4500</leader><controlfield tag="001">9780691234670</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20210830012106.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">210830t20211996nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780691234670</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9780691234670</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)589790</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QC174.17.G7</subfield><subfield code="b">C37 1995eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT002010</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530.1/2/0151255</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Carter, J. Scott, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The Classical and Quantum 6j-symbols. (MN-43), Volume 43 /</subfield><subfield code="c">Masahico Saito, Daniel E. Flath, J. Scott Carter.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2021]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (176 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematical Notes ;</subfield><subfield code="v">109</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Foreword -- </subfield><subfield code="t">1 Introduction -- </subfield><subfield code="t">2 Representations of U(sl(2)) -- </subfield><subfield code="t">3 Quantum sl(2) -- </subfield><subfield code="t">4 The Quantum Trace and Color Representations -- </subfield><subfield code="t">5 The Turaev-Viro Invariant -- </subfield><subfield code="t">References</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals. The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Quantum groups.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Representations of groups.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Algebra / Abstract.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Flath, Daniel E., </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Saito, Masahico, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Archive 1927-1999</subfield><subfield code="z">9783110442496</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9780691234670?locatt=mode:legacy</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9780691234670</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/cover/covers/9780691234670.jpg</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999</subfield><subfield code="c">1927</subfield><subfield code="d">1999</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield></record></collection> |