On the String Lie Algebra

被引：2

作者：

Riviere, Salim ^{[1
]}

Wagemann, Friedrich ^{[2
]}

机构：

[1] Univ Luxembourg, Walferdange, Luxembourg

[2] Univ Nantes, Nantes, France

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2015年 / 18卷 / 04期

关键词：

Crossed modules of Lie algebras; String Lie algebra; Quasi-invariant tensors; Categorification of an r-matrix;

D O I：

10.1007/s10468-015-9533-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct an abelian representative for the crossed module associated to the string Lie algebra. We show how to apply this construction in order to define quasi-invariant tensors which serve to categorify the infinitesimal braiding on the category of g-modules given by an r-matrix, following Cirio-Martins.

引用

页码：1071 / 1099

页数：29

共 50 条

[31] Hom-Lie group and hom-Lie algebra from Lie group and Lie algebra perspective
Merati, S.
Farhangdoost, M. R.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2021, 18 (05)
[32] On the Torelli Lie algebra
Kupers, Alexander
Randal-Williams, Oscar
FORUM OF MATHEMATICS PI, 2023, 11
[33] On the multiplier of a Lie algebra
Yankosky, B
JOURNAL OF LIE THEORY, 2003, 13 (01) : 1 - 6
[34] An atavistic Lie algebra
Fairlie, DB
Zachos, CK
PHYSICS LETTERS B, 2006, 637 (1-2) : 123 - 127
[35] A GROUP OF A LIE ALGEBRA
HEEREMA, N
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1970, 244 : 112 - &
[36] Lie algebra of transposition
Marin, Ivan
JOURNAL OF ALGEBRA, 2007, 310 (02) : 742 - 774
[37] ON THE RADICAL OF A LIE ALGEBRA
HARISHCHANDRA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 1 (01) : 14 - 17
[38] STRING FIELD ALGEBRA
AREFEVA, IY
VOLOVICH, IV
PHYSICS LETTERS B, 1986, 182 (3-4) : 312 - 316
[39] ON LIE ALGEBRA ACTIONS
Cushman, Richard H.
Sniatycki, Jedrzej
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2020, 13 (04): : 1115 - 1129
[40] On the mirabolic Lie algebra
Kirillov, A. A.
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2014, 48 (02) : 145 - 149

← 1 2 3 4 5 →