"Birman–Murakami-Wenzl algebra"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==encyclopedia== * http://en.wikipedia.org/wiki/Brauer_algebra 분류:Lie theory) |
Pythagoras0 (토론 | 기여) |
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| + | ==introduction== | ||
| + | * Birman–Murakami-Wenzl algebra, a deformation of the Brauer algebra. | ||
| + | * has the Hecke algebra of type A as a quotient | ||
| + | * its specializations play a role in types B,C,D akin to that of the symmetric group in Schur-Weyl duality | ||
| + | |||
| + | ==history== | ||
| + | * In 1984, Vaughan Jones introduced a new polynomial invariant of link isotopy types which is called the Jones polynomial. | ||
| + | * The invariants are related to the traces of irreducible representations of Hecke algebras associated with the symmetric groups. | ||
| + | * In 1986, Murakami (1986) showed that the Kauffman polynomial can also be interpreted as a function F on a certain associative algebra. | ||
| + | * In 1989, Birman & Wenzl (1989) constructed a two-parameter family of algebras <math>C_n(\ell, m)</math> with the Kauffman polynomial <math>K_n(\ell, m)</math> as trace after appropriate renormalization. | ||
| + | |||
| + | |||
| + | ==related items== | ||
| + | * [[Schur-Weyl duality for general linear groups]] | ||
| + | |||
| + | |||
| + | ==expositions== | ||
| + | * Ariki, Susumu. 2006. “Algebras Arising from Schur-Weyl Type Dualities.” In Proceedings of the 38th Symposium on Ring Theory and Representation Theory, 1–10. Symp. Ring Theory Represent. Theory Organ. Comm., Yamanashi. http://www.ams.org/mathscinet-getitem?mr=2264119. | ||
| + | * Benkart, Georgia. 1996. “Commuting Actions—a Tale of Two Groups.” In Lie Algebras and Their Representations (Seoul, 1995), 194:1–46. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=1395593. | ||
| + | * Schüler, Axel. 1993. “The Brauer Algebra and the Birman-Wenzl-Murakami Algebra.” Seminar Sophus Lie 3 (1): 3–11. http://www.heldermann-verlag.de/jlt/jlt03/SCHUELAT.PDF | ||
| + | |||
| + | |||
| + | ==articles== | ||
| + | * Rui, Hebing, and Linliang Song. “Mixed Schur-Weyl Duality between General Linear Lie Algebras and Cyclotomic Walled Brauer Algebras.” arXiv:1509.05855 [math], September 19, 2015. http://arxiv.org/abs/1509.05855. | ||
| + | * Rui, Hebing, and Linliang Song. ‘Decomposition Matrices of Birman-Murakami-Wenzl Algebras’. arXiv:1411.3067 [math], 11 November 2014. http://arxiv.org/abs/1411.3067. | ||
| + | * Li, Ge. “A KLR Grading of the Brauer Algebras.” arXiv:1409.1195 [math], September 3, 2014. http://arxiv.org/abs/1409.1195. | ||
| + | * Morton, H. R. “A Basis for the Birman-Wenzl Algebra.” arXiv:1012.3116 [math], December 14, 2010. http://arxiv.org/abs/1012.3116. | ||
| + | |||
==encyclopedia== | ==encyclopedia== | ||
* http://en.wikipedia.org/wiki/Brauer_algebra | * http://en.wikipedia.org/wiki/Brauer_algebra | ||
| + | * http://en.wikipedia.org/wiki/Birman–Wenzl_algebra | ||
[[분류:Lie theory]] | [[분류:Lie theory]] | ||
| + | [[분류:migrate]] | ||
| + | |||
| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q2835973 Q2835973] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LEMMA': 'period'}] | ||
2021년 2월 17일 (수) 01:38 기준 최신판
introduction
- Birman–Murakami-Wenzl algebra, a deformation of the Brauer algebra.
- has the Hecke algebra of type A as a quotient
- its specializations play a role in types B,C,D akin to that of the symmetric group in Schur-Weyl duality
history
- In 1984, Vaughan Jones introduced a new polynomial invariant of link isotopy types which is called the Jones polynomial.
- The invariants are related to the traces of irreducible representations of Hecke algebras associated with the symmetric groups.
- In 1986, Murakami (1986) showed that the Kauffman polynomial can also be interpreted as a function F on a certain associative algebra.
- In 1989, Birman & Wenzl (1989) constructed a two-parameter family of algebras \(C_n(\ell, m)\) with the Kauffman polynomial \(K_n(\ell, m)\) as trace after appropriate renormalization.
expositions
- Ariki, Susumu. 2006. “Algebras Arising from Schur-Weyl Type Dualities.” In Proceedings of the 38th Symposium on Ring Theory and Representation Theory, 1–10. Symp. Ring Theory Represent. Theory Organ. Comm., Yamanashi. http://www.ams.org/mathscinet-getitem?mr=2264119.
- Benkart, Georgia. 1996. “Commuting Actions—a Tale of Two Groups.” In Lie Algebras and Their Representations (Seoul, 1995), 194:1–46. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=1395593.
- Schüler, Axel. 1993. “The Brauer Algebra and the Birman-Wenzl-Murakami Algebra.” Seminar Sophus Lie 3 (1): 3–11. http://www.heldermann-verlag.de/jlt/jlt03/SCHUELAT.PDF
articles
- Rui, Hebing, and Linliang Song. “Mixed Schur-Weyl Duality between General Linear Lie Algebras and Cyclotomic Walled Brauer Algebras.” arXiv:1509.05855 [math], September 19, 2015. http://arxiv.org/abs/1509.05855.
- Rui, Hebing, and Linliang Song. ‘Decomposition Matrices of Birman-Murakami-Wenzl Algebras’. arXiv:1411.3067 [math], 11 November 2014. http://arxiv.org/abs/1411.3067.
- Li, Ge. “A KLR Grading of the Brauer Algebras.” arXiv:1409.1195 [math], September 3, 2014. http://arxiv.org/abs/1409.1195.
- Morton, H. R. “A Basis for the Birman-Wenzl Algebra.” arXiv:1012.3116 [math], December 14, 2010. http://arxiv.org/abs/1012.3116.
encyclopedia
메타데이터
위키데이터
- ID : Q2835973
Spacy 패턴 목록
- [{'LEMMA': 'period'}]