Convolution bialgebra of a Lie groupoid and transversal

被引：2

作者：

Kalisnik, J. ^{[1
,2
]}

Mrcun, J. ^{[1
,2
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Jadranska 19, Ljubljana 1000, Slovenia

[2] Univ Ljubljana, Inst Math Phys & Mech, Jadranska 19, Ljubljana 1000, Slovenia

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2022年 / 180卷

关键词：

Lie groupoid; Lie algebroid; Convolution algebra; Universal enveloping algebra; Transversal distribution; ETALE GROUPOIDS; HOPF ALGEBROIDS;

D O I：

10.1016/j.geomphys.2022.104642

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a Lie groupoid W over a smooth manifold M we construct the adjoint action of the etale Lie groupoid W# of germs of local bisections of W on the Lie algebroid g of W. With this action, we form the associated convolution C-c(infinity)(M)/R-bialgebra C-c(infinity)(W-#, g). We represent this C-c(infinity)(M)/R-bialgebra in the algebra of transversal distributions on W. This construction extends the Cartier-Gabriel decomposition of the Hopf algebra of distributions with finite support on a Lie group. (C) 2022 Elsevier B.V. All rights reserved.

引用

页数：20