On a Lie Algebraic Approach to Abelian Extensions of Associative Algebras

Tan, Youjun; Xu, Senrong

doi:10.4153/s0008439520000193

Can. Math. Bull.

2020

DOI: 10.4153/s0008439520000193

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On a Lie Algebraic Approach to Abelian Extensions of Associative Algebras

Youjun Tan¹,

Senrong Xu

Abstract: By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian extension of an associative algebra.

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2024

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Cited by 2 publications

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Associative 2-algebras and nonabelian extensions of associative algebras

Sheng,

Wang

2024

J. Homotopy Relat. Struct.

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Associative 2-algebras and nonabelian extensions of associative algebras

Sheng,

Wang

2024

J. Homotopy Relat. Struct.

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Wells-type exact sequence and crossed extensions of algebras with bracket

Casas,

Khmaladze,

Ladra

2024

Forum Mathematicum

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We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second cohomology. Finally, we construct an eight-term exact sequence in the cohomology of algebras with bracket.

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On a Lie Algebraic Approach to Abelian Extensions of Associative Algebras

Abstract: By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian extension of an associative algebra.

Cited by 2 publications

References 12 publications

Associative 2-algebras and nonabelian extensions of associative algebras

Associative 2-algebras and nonabelian extensions of associative algebras

Wells-type exact sequence and crossed extensions of algebras with bracket

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