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Representations and (2,3)-Cohomology of Bol Algebras with Applications
Journal of Lie theory, Tome 34 (2024) no. 1, pp. 171-192
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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.
Classification : 17A40, 17B10, 17B56, 17D99
Mots-clés : Representation, cohomology, deformation, abelian extension, Bol algebra 
@article{JLT_2024_34_1_JLT_2024_34_1_a7,
     author = {A. N. Issa},
     title = {Representations and {(2,3)-Cohomology} of {Bol} {Algebras} with {Applications}},
     journal = {Journal of Lie theory},
     pages = {171--192},
     year = {2024},
     volume = {34},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2024_34_1_JLT_2024_34_1_a7/}
}
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A. N. Issa. Representations and (2,3)-Cohomology of Bol Algebras with Applications. Journal of Lie theory, Tome 34 (2024) no. 1, pp. 171-192. http://geodesic.mathdoc.fr/item/JLT_2024_34_1_JLT_2024_34_1_a7/