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arXiv · 2210.11397

Representations and (2,3)-cohomology of Bol algebras with applications

A. Nourou Issa
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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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A. Nourou Issa. 2022-10-20. Representations and (2,3)-cohomology of Bol algebras with applications. https://arxiv.org/abs/2210.11397

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