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Journal of Lie Theory 34 (2024), No. 1, 171--192
Copyright Heldermann Verlag 2024

Representations and (2,3)-Cohomology of Bol Algebras with Applications

A. Nourou Issa
Département de Mathématiques, Université d'Abomey-Calavi, Cotonou, Benin

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.

Keywords: Representation, cohomology, deformation, abelian extension, Bol algebra.

MSC: 17A40, 17B10, 17B56, 17D99.

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