Cohomology Theory of Nonassociative Algebras with Metagroup Relations

Cohomology Theory of Nonassociative Algebras with Metagroup Relations

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...

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Bibliographic Details
Main Author: Sergey V. Ludkowski
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Axioms
Subjects:
nonassociative algebra
cohomology
extension
metagroup
Online Access:https://www.mdpi.com/2075-1680/8/3/78
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spelling doaj-783b84870195456184887df6f8ed82f72020-11-25T01:45:41ZengMDPI AGAxioms2075-16802019-07-01837810.3390/axioms8030078axioms8030078Cohomology Theory of Nonassociative Algebras with Metagroup RelationsSergey V. Ludkowski0Department of Applied Mathematics, MIREA—Russian Technological University, av. Vernadsky 78, 119454 Moscow, RussiaNonassociative 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.https://www.mdpi.com/2075-1680/8/3/78nonassociative algebracohomologyextensionmetagroup
collection DOAJ
language English
format Article
sources DOAJ
author Sergey V. Ludkowski
spellingShingle Sergey V. Ludkowski
Cohomology Theory of Nonassociative Algebras with Metagroup Relations
Axioms
nonassociative algebra
cohomology
extension
metagroup
author_facet Sergey V. Ludkowski
author_sort Sergey V. Ludkowski
title Cohomology Theory of Nonassociative Algebras with Metagroup Relations
title_short Cohomology Theory of Nonassociative Algebras with Metagroup Relations
title_full Cohomology Theory of Nonassociative Algebras with Metagroup Relations
title_fullStr Cohomology Theory of Nonassociative Algebras with Metagroup Relations
title_full_unstemmed Cohomology Theory of Nonassociative Algebras with Metagroup Relations
title_sort cohomology theory of nonassociative algebras with metagroup relations
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2019-07-01
description 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.
topic nonassociative algebra
cohomology
extension
metagroup
url https://www.mdpi.com/2075-1680/8/3/78
work_keys_str_mv AT sergeyvludkowski cohomologytheoryofnonassociativealgebraswithmetagrouprelations
_version_ 1725023403433263104

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