Representations and (2,3)-cohomology of Bol algebras with applications
A. Nourou Issa
TL;DR
This paper develops a representation theory and a (2,3)-cohomology framework for Bol algebras, exploring their deformations and extensions, and providing new tools for their structural analysis.
Contribution
It introduces a novel (2,3)-cohomology theory for Bol algebras and applies it to study deformations and abelian extensions.
Findings
Characterized infinitesimal deformations via (2,3)-cocycles
Defined a (2,3)-cohomology group for Bol algebras
Applied cohomology to classify abelian extensions
Abstract
A representation theory for Bol algebras is proposed. For a suitable (2,3)-cohomology theory for Bol algebras, we define a (2,3)-coboundary with companion and next we define a (2,3)-cohomology group. Deformations of Bol algebras are investigated. In particular, one-parameter infinitesimal deformations of Bol algebras are characterized in terms of Bol algebras of deformation type and (2,3)-cocycles with coefficients in the adjoint representation. The (2,3)-cohomology group is also applied to study abelian extensions of Bol algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons