Skew-symmetric hom-algebroids and their representation theory

Abstract

In this paper, we introduce skew-symmetric hom-algebroids and linear almost Poisson structures on dual hom-bundles. In addition, we show that these two geometric notions are related to each other and present several interesting examples of them. Moreover, we study the representation theory of skew-symmetric hom-algebroids and their dual spaces. Finally, we give the notion of phase spaces of skew-symmetric algebroids.