Atiyah Classes of Lie Bialgebras

被引：0

作者：

Hong, Wei ^{[1
,2
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

[2] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Hubei, Peoples R China

来源：

JOURNAL OF LIE THEORY | 2019年 / 29卷 / 01期

关键词：

Atiyah class; Lie bialgebras; Lie algebra pair; ROZANSKY-WITTEN INVARIANTS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Atiyah class was originally introduced by M. F. Atiyah. It has many developments in recent years. One important case is the Atiyah classes of Lie algebra pairs. In this paper, we study the Atiyah class of the Lie algebra pair associated with a Lie bialgebra (g, g*) . A simple description of the Atiyah class and the first scalar Atiyah class is given by the Lie algebra structures on g and g* . As an application, the Atiyah classes for some special cases are investigated.

引用

页码：263 / 275

页数：13

共 50 条

[41] On Quantizable Odd Lie Bialgebras
Khoroshkin, Anton
Merkulov, Sergei
Willwacher, Thomas
LETTERS IN MATHEMATICAL PHYSICS, 2016, 106 (09) : 1199 - 1215
[42] Factorizable Lie Bialgebras, Quadratic Rota-Baxter Lie Algebras and Rota-Baxter Lie Bialgebras
Lang, Honglei
Sheng, Yunhe
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2023, 397 (02) : 763 - 791
[43] Quantization of Lie bialgebras revisited
Severa, Pavol
SELECTA MATHEMATICA-NEW SERIES, 2016, 22 (03): : 1563 - 1581
[44] On simple real Lie bialgebras
Andruskiewitsch, N
Jancsa, P
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (03) : 139 - 158
[45] On the associative analog of Lie bialgebras
Aguiar, M
JOURNAL OF ALGEBRA, 2001, 244 (02) : 492 - 532
[46] Hamiltonian type Lie bialgebras
Bin Xin
Guang-ai Song
Yu-cai Su
Science in China Series A: Mathematics, 2007, 50 : 1267 - 1279
[47] LIE BIALGEBRAS MODULES AND COHOMOLOGY
LECOMTE, PBA
ROGER, C
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1990, 310 (06): : 405 - 410
[48] Extending Structures for Lie Bialgebras
Hong, Yanyong
JOURNAL OF LIE THEORY, 2023, 33 (03) : 783 - 798
[49] Quantization of inhomogeneous Lie bialgebras
Kulish, PP
Mudrov, AI
JOURNAL OF GEOMETRY AND PHYSICS, 2002, 42 (1-2) : 64 - 77
[50] Quantization of Lie bialgebras, III
Etingof P.
Kazhdan D.
Selecta Mathematica, 1998, 4 (2) : 233 - 269

← 1 2 3 4 5 →