Quiver Hecke Algebras and 2-Lie Algebras

被引：93
|
作者：
Rouquier, Raphael [1 ,2 ]
机构：
[1] Univ Oxford, Math Inst, Oxford OX1 3LB, England
[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
来源：
ALGEBRA COLLOQUIUM | 2012年 / 19卷 / 02期
关键词：
Lie algebras; Hecke algebras; representations; quiver varieties; QUANTUM; CATEGORIFICATION; SL(2);
D O I：
10.1142/S1005386712000247
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.
引用
收藏
页码：359 / 410
页数：52
相关论文
共 50 条
  • [21] Quiver Schur algebras and Koszul duality
    Maksimau, Ruslan
    JOURNAL OF ALGEBRA, 2014, 406 : 91 - 133
  • [22] CENTRALIZER ALGEBRAS AND DEGENERATE AFFINE HECKE ALGEBRAS
    Ellers, Harald
    Murray, John
    COMMUNICATIONS IN ALGEBRA, 2014, 42 (03) : 1074 - 1094
  • [23] Buildings and Hecke algebras
    Parkinson, J
    JOURNAL OF ALGEBRA, 2006, 297 (01) : 1 - 49
  • [24] Lie algebras with BCL algebras
    Liu, Yonghong
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2018, 11 (02): : 444 - 448
  • [25] Leibniz Algebras and Lie Algebras
    Mason, Geoffrey
    Yamskulna, Caywalee
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2013, 9
  • [26] On representations of Hecke algebras
    Isaev, AP
    Ogievetsky, O
    CZECHOSLOVAK JOURNAL OF PHYSICS, 2005, 55 (11) : 1433 - 1441
  • [27] FREE PROBABILITY ON C*-ALGEBRAS INDUCED BY HECKE ALGEBRAS OVER PRIMES
    Cho, Ilwoo
    Jorgense, Palle
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2019, 12 (08): : 2221 - 2252
  • [28] Hecke-Clifford algebras and spin Hecke algebras III: The trigonometric type
    Khongsap, Ta
    JOURNAL OF ALGEBRA, 2009, 322 (08) : 2731 - 2750
  • [29] Idempotents of Hecke algebras of type A.
    Aiston, AK
    Morton, HR
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 1998, 7 (04) : 463 - 487
  • [30] LANGLANDS PARAMETERS, FUNCTORIALITY AND HECKE ALGEBRAS
    Solleveld, Maarten
    PACIFIC JOURNAL OF MATHEMATICS, 2020, 304 (01) : 209 - 302
12345