"Birman–Murakami-Wenzl algebra"의 두 판 사이의 차이
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* has the Hecke algebra of type A as a quotien | * has the Hecke algebra of type A as a quotien | ||
* its specializations play a role in types B,C,D akin to that of the symmetric group in Schur-Weyl duality | * its specializations play a role in types B,C,D akin to that of the symmetric group in Schur-Weyl duality | ||
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| + | ==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. | ||
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==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]] | ||
2014년 8월 6일 (수) 21:36 판
introduction
- Birman–Murakami-Wenzl algebra, a deformation of the Brauer algebra.
- has the Hecke algebra of type A as a quotien
- 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