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

[41] Lie algebra fermions
Troost, Jan
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2020, 53 (42)
[42] The string little algebra
Glennon, Keith
West, Peter
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2022, 37 (10):
[43] ABELIANIZATIONS OF DERIVATION LIE ALGEBRAS OF THE FREE ASSOCIATIVE ALGEBRA AND THE FREE LIE ALGEBRA
Morita, Shigeyuki
Sakasai, Takuya
Suzuki, Masaaki
DUKE MATHEMATICAL JOURNAL, 2013, 162 (05) : 965 - 1002
[44] The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
Bremner, Murray R.
Douglas, Andrew
JOURNAL OF ALGEBRA, 2012, 358 : 269 - 291
[45] Post-Lie Algebra Structures on the Lie Algebra gl(2, C)
Sheng, Yuqiu
Tang, Xiaomin
ABSTRACT AND APPLIED ANALYSIS, 2013,
[46] A new Lie algebra along with its induced Lie algebra and associated with applications
Feng, Binlu
Liu, Jiaqi
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (04) : 1734 - 1741
[47] Leibniz and Lie algebra structures for Nambu algebra
Daletskii, YL
Takhtajan, LA
LETTERS IN MATHEMATICAL PHYSICS, 1997, 39 (02) : 127 - 141
[48] Computing the maximal algebra of quotients of a Lie algebra
Bresar, Matej
Perera, Francesc
Sanchez Ortega, Juana
Siles Molina, Mercedes
FORUM MATHEMATICUM, 2009, 21 (04) : 601 - 620
[49] THE CENTRALIZER OF A LIE-ALGEBRA IN AN ENVELOPING ALGEBRA
JOHNSON, KD
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1989, 395 : 196 - 201
[50] Leibniz and Lie Algebra Structures for Nambu Algebra
Yuri L. Daletskii
Leon A. Takhtajan
Letters in Mathematical Physics, 1997, 39 : 127 - 141

← 1 2 3 4 5 →