Last Multipliers on Lie Algebroids

Proceedings Mathematical Sciences

Cristina-Elena HreÅ£canu²  Mircea Crasmareanu¹ 

[1] Al. I. Cuza University, Faculty of Mathematics, IaÅŸi 000, România$$;Åžtefan cel Mare University, Suceava, România$$

关键词: Liouville equation;    volume form;    last multiplier;    Lie algebroid;    Gerstenhaber algebra;    Schouten bracket;    exact section;    Casimir function;    Witten differential;    Marsden differential.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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.

【 授权许可】

Unknown