Extensions of Lie brackets

被引：21

作者：

Brahic, Olivier ^{[1
]}

机构：

[1] Univ Tecn Lisboa, Dept Matemat, Inst Super Tecn, P-1049001 Lisbon, Portugal

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2010年 / 60卷 / 02期

关键词：

Lie algebroids; Lie groupoids; Extensions; POISSON COHOMOLOGY; INTEGRABILITY;

D O I：

10.1016/j.geomphys.2009.10.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a framework for extensions of Lie algebroids, including non-abelian extensions and Lie algebroids over different bases. Our approach involves Ehresmann connections, which allows straight generalizations of classical constructions. We exhibit a filtration in cohomology and explain the associated spectral sequence. We also give a description of the groupoid integrating an extension in case a complete connection exists. The integrability is also studied. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：352 / 374

页数：23

共 26 条

[1]

[Anonymous], [No title captured]

[2]

[Anonymous], 1987, LIE GROUPOIDS LIE AL

[3]

BEHREND K, MATHDG0605694

[4]

Brahic O., INTEGRATION CO UNPUB

[5]

Brahic O, 2008, CONTEMP MATH, V450, P41

[6]

CANNAS DA SILVA A., 1999, Geometric models for noncommutative algebras, V10

[7]

Cattaneo AS, 2001, PROG MATH, V198, P61

[8] On (co-)morphisms of Lie pseudoalgebras and groupoids [J].

Chen, Z. ;

Liu, Z.-J. .

JOURNAL OF ALGEBRA, 2007, 316 (01) :1-31

[9] Integrability of Lie brackets [J].

Crainic, M ;

Fernandes, RL .

ANNALS OF MATHEMATICS, 2003, 157 (02) :575-620

[10]

CRAINIC M, 2005, J SYMPLECT GEOM, V2, P579

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