Cohomology Theory of Nonassociative Algebras with Metagroup Relations

Abstract

Nonassociative algebras with metagroup relations and their modules are studied. Their cohomology theory is scrutinized. Extensions and cleftings of these algebras are studied. Broad families of such algebras and their acyclic complexes are described. For this purpose, different types of products of metagroups are investigated. Necessary structural properties of metagroups are studied. Examples are given. It is shown that a class of nonassociative algebras with metagroup relations contains a subclass of generalized Cayley−Dickson algebras.

Keywords

• nonassociative algebra
• cohomology
• extension
• metagroup