Algebraic constructions for Jacobi-Jordan algebras
A. L. Agore, G. Militaru

TL;DR
This paper develops algebraic tools and classifications for Jacobi-Jordan algebras, including cohomological objects, product constructions, and applications to extensions and supersolvability.
Contribution
It introduces a cohomological classification framework and unified product constructions for Jacobi-Jordan algebras, expanding understanding of their extensions and structure.
Findings
Classification of Jacobi-Jordan algebra extensions using cohomology
Introduction of unified and bicrossed product constructions
Description of Galois groups and an Artin-type theorem for these algebras
Abstract
For a given Jacobi-Jordan algebra and a vector space over a field , a non-abelian cohomological type object is constructed: it classifies all Jacobi-Jordan algebras containing as a subalgebra of codimension equal to . Any such algebra is isomorphic to a so-called \emph{unified product} . Furthermore, we introduce the bicrossed (semi-direct, crossed, or skew crossed) product 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 is described as a subgroup of the semidirect product of groups and an Artin type theorem for Jacobi-Jordan algebra is proven. The key tools for classifying supersolvable and flag…
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
