交错代数双模的无穷小形变

Infinitesimal Deformation of the Bimodules over Alternative Algebras

本文主要研究交错代数双模的无穷小形变。讨论了交错代数的形变,给出了交错代数双模的无穷小形变的定义,讨论两个无穷小形变的等价条件和双模的无穷小形变是平凡的条件。文章的最后给出了交错代数上Nijenhuis算子的定义,并且找到交错代数双模的平凡形变与Nijenhuis算子结构的关系。

In this paper, we study the infinitesimal deformation of the bimodules over alternative algebras. The deformation of alternative algebra is discussed, and the definition of infinitesimal deformation of the bimodules over alternative algebras is given. The equivalent conditions of two infinitesimal deformations are discussed. We also discuss the conditions that make infinitesimal deformation of the bimodules be trivial. At the end of the paper, the Nijenhuis operators of alternative algebras are defined, and the relationship between trivial deformation and Nijenhuis operator structure is also found.