Algebraic constructions for Jacobi-Jordan algebras

For a given Jacobi-Jordan algebra A and a vector space V over a field k, a non-abelian cohomological type object HA2(V,A) is constructed: it classifies all Jacobi-Jordan algebras containing A as a subalgebra of codimension equal to dimk(V). Any such algebra is isomorphic to a so-called unified produ...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 630; pp. 158 - 178
Main Authors Agore, A.L., Militaru, G.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.12.2021
American Elsevier Company, Inc
Subjects
Algebra
Bicrossed products
Fields (mathematics)
Jacobi-Jordan algebras
Linear algebra
Matched pairs
Subgroups
Unified products
17A01
17C10
17C55
Unified products
Bicrossed products
Matched pairs
Jacobi-Jordan algebras
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Summary:For a given Jacobi-Jordan algebra A and a vector space V over a field k, a non-abelian cohomological type object HA2(V,A) is constructed: it classifies all Jacobi-Jordan algebras containing A as a subalgebra of codimension equal to dimk(V). Any such algebra is isomorphic to a so-called unified productA♮V. Furthermore, we introduce the bicrossed (semi-direct, crossed, or skew crossed) product A⋈V associated to two Jacobi-Jordan algebras as a special case of the unified product. Several examples and applications are provided: the Galois group of the extension A⊆A⋈V is described as a subgroup of the semidirect product of groups GLk(V)⋊Homk(V,A) and an Artin type theorem for Jacobi-Jordan algebra is proven.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.08.003