REPRESENTATIONS OF FINITE-DIMENSIONAL QUOTIENT ALGEBRAS OF THE 3-STRING BRAID GROUP

被引：0

作者：

Pyatov, Pavel ^{[1
,2
]}

Trofimova, Anastasia ^{[1
,3
]}

机构：

[1] Natl Res Univ, Higher Sch Econ, 20 Myasnitskaya St, Moscow 101000, Russia

[2] Joint Inst Nucl Res, Bogoliubov Lab Theoret Phys, Dubna 141980, Moscow Region, Russia

[3] Skolkovo Inst Sci & Technol, Ctr Adv Studies, Moscow, Russia

来源：

MOSCOW MATHEMATICAL JOURNAL | 2021年 / 21卷 / 02期

关键词：

Braid group; irreducible representations; semisimplicity; COMPLEX REFLECTION GROUPS; FREENESS CONJECTURE; HECKE ALGEBRAS;

D O I：

10.17323/1609-4514-2021-21-2-427-442

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider quotients of the group algebra of the 3-string braid group B-3 by p-th order generic polynomial relations on the elementary braids. If p = 2, 3, 4, 5, these quotient algebras are finite dimensional. We give semisimplicity criteria for these algebras and present explicit formulas for all their irreducible representations.

引用

页码：427 / 442

页数：16

共 50 条

[1] Quilts, the 3-string braid group, and braid actions on finite groups: An introduction
Hsu, T
MONSTER AND LIE ALGEBRAS, 1998, 7 : 85 - 97
[2] MODULI OF REPRESENTATIONS OF FINITE-DIMENSIONAL ALGEBRAS
KING, AD
QUARTERLY JOURNAL OF MATHEMATICS, 1994, 45 (180): : 515 - 530
[3] FINITE-DIMENSIONAL REPRESENTATIONS OF PI ALGEBRAS
AMITSUR, SA
SMALL, LW
JOURNAL OF ALGEBRA, 1990, 133 (02) : 244 - 248
[4] Representations of finite-dimensional Hopf algebras
Lorenz, M
JOURNAL OF ALGEBRA, 1997, 188 (02) : 476 - 505
[5] Decomposing moduli of representations of finite-dimensional algebras
Chindris, Calin
Kinser, Ryan
MATHEMATISCHE ANNALEN, 2018, 372 (1-2) : 555 - 580
[6] Finite-dimensional representations of quantum affine algebras
Akasaka, T
Kashiwara, M
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1997, 33 (05) : 839 - 867
[7] Finite-dimensional representations of rational Cherednik algebras
Berest, Y
Etingof, P
Ginzburg, V
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2003, 2003 (19) : 1053 - 1088
[8] FINITE-DIMENSIONAL REPRESENTATIONS OF W-ALGEBRAS
Losev, Ivan
DUKE MATHEMATICAL JOURNAL, 2011, 159 (01) : 99 - 143
[9] Decomposing moduli of representations of finite-dimensional algebras
Calin Chindris
Ryan Kinser
Mathematische Annalen, 2018, 372 : 555 - 580
[10] Finite-dimensional representations of Leavitt path algebras
Koc, Ayten
Ozaydin, Murad
FORUM MATHEMATICUM, 2018, 30 (04) : 915 - 928

← 1 2 3 4 5 →