Last multipliers on Lie algebroids

被引：0
作者：
Mircea Crasmareanu
Cristina-Elena Hreţcanu
机构：
[1] Al. I. Cuza University,Faculty of Mathematics
[2] Ştefan cel Mare University,undefined
来源：
Proceedings - Mathematical Sciences | 2009年 / 119卷
关键词：
Liouville equation; volume form; last multiplier; Lie algebroid; Gerstenhaber algebra; Schouten bracket; exact section; Casimir function; Witten differential; Marsden differential;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper we extend the theory of last multipliers as solutions of the Liouville’s transport equation to Lie algebroids with their top exterior power as trivial line bundle (previously developed for vector fields and multivectors). We define the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed last multiplier is still a Gerstenhaber subalgebra). We present some characterizations of this extension in terms of Witten and Marsden differentials.
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页码：287 / 296
页数：9
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