标题： 斜代数胚关系的模类 显示英文标题

标题： Modular classes of skew algebroid relations

摘要： 斜代数胚是李代数胚概念的自然推广。 在本文中，对于一个斜代数胚E，其模类mod(E)在经典以及超几何表述中都被定义。 证明了当且仅当E是模的，即mod(E)=0时，E*上存在一个均匀的处处不为零的1密度，该密度对于所有哈密顿向量场都是不变的。 此外，引入并研究了子代数胚的相对模类及其在整体结构中的应用，以及斜代数胚关系的模类。 这些概念特别提供了一种统一的方法来处理李代数胚同态的模类和泊松映射的模类的概念。 显示英文摘要

摘要： Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.