English

(Co)homology of compatible associative algebras

Rings and Algebras 2021-07-21 v1 K-Theory and Homology Representation Theory

Abstract

In this paper, we define and study (co)homology theories of a compatible associative algebra AA. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define the cohomology of a compatible associative algebra AA and as applications, we study extensions, deformations and extensibility of finite order deformations of AA. We end this paper by considering compatible presimplicial vector spaces and the homology of compatible associative algebras.

Keywords

Cite

@article{arxiv.2107.09259,
  title  = {(Co)homology of compatible associative algebras},
  author = {Taoufik Chtioui and Apurba Das and Sami Mabrouk},
  journal= {arXiv preprint arXiv:2107.09259},
  year   = {2021}
}

Comments

28 pages; comments are welcome