Derivations and the first cohomology group of trivial extension algebras

DOI10.1007/s00009-017-0949-zzbMath1373.16022arXiv1604.02758OpenAlexW2963741070MaRDI QIDQ1679144

Brahim Fahid, Driss Bennis

Publication date: 8 November 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.02758

zbMATH Keywords

inner derivationderivationcohomology grouptriangular matrix algebratrivial extension algebracentral inner bimodule homomorphismmodule generalized derivation

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Derivations, actions of Lie algebras (16W25) Centralizing and normalizing extensions (16S20)

Related Items

Unnamed Item, Poisson cohomology of trivial extension algebras, Lie triple derivations on trivial extension algebras, Commuting mappings on the Hochschild extension of an algebra, Jordan centralizer maps on trivial extension algebras, On generalized Lie derivations, Lie generalized derivations on trivial extension algebras, Poisson derivations and the first Poisson cohomology group on trivial extension algebras, The first cohomology group and weak amenability of a Morita context Banach algebra

Cites Work

• Jordan derivations on trivial extensions
• The first cohomology group of module extension Banach algebras
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• Derivations of upper triangular matrix rings
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• COHOMOLOGY OF SPLIT ALGEBRAS AND OF TRIVIAL EXTENSIONS This work has been supported by the projects SECYT-ECOS A98E05 and SECYT-CAPES BR1299OG. The first author wishes to thank FAPESP (Brazil) for financial support. The second author has a research scholarship from Cnpq (Brazil). The third and fourth authors are research members of CONICET (Argentina).
• Derivations of triangular Banach algebras
• Automorphism groups of trivial extensions.
• Hochschild cohomology of relation extension algebras