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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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 |