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Open AccessArticle

Cohomology Theory of Nonassociative Algebras with Metagroup Relations

Department of Applied Mathematics, MIREA—Russian Technological University, av. Vernadsky 78, 119454 Moscow, Russia
Axioms 2019, 8(3), 78; https://doi.org/10.3390/axioms8030078
Received: 30 April 2019 / Revised: 21 June 2019 / Accepted: 24 June 2019 / Published: 4 July 2019
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
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PDF [372 KB, uploaded 9 July 2019]

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. View Full-Text
Keywords: nonassociative algebra; cohomology; extension; metagroup nonassociative algebra; cohomology; extension; metagroup
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ludkowski, S.V. Cohomology Theory of Nonassociative Algebras with Metagroup Relations. Axioms 2019, 8, 78.

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