On the cohomology of an algebra morphism

DOI10.1016/0021-8693(85)90104-8zbMath0595.16021OpenAlexW2012574112MaRDI QIDQ1077510

Samuel D. Schack, Murray Gerstenhaber

Publication date: 1985

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(85)90104-8

zbMATH Keywords

equivalenceexact sequencesnatural transformationcontravariant functorcohomological aspects of an algebra morphismCohomology comparison theoremdiagram of \(k\)-algebrasHochschild cochain complexHochschild cohomologiespresheaf of bimodulesrelative Yoneda cohomologyYoneda cohomology theory

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30)

Related Items

Deformation of Dual Leibniz Algebra Morphisms ⋮ Homological epimorphisms, recollements and Hochschild cohomology -- with a conjecture by Snashall-Solberg in view ⋮ $\alpha$-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras ⋮ Deformations of coalgebra morphisms. ⋮ Morphisms Cohomology and Deformations of Hom-algebras ⋮ \(\mathcal G_{\infty}\)-structure on the deformation complex of a morphism ⋮ Deformation Theory of Dialgebra Morphisms ⋮ Equivariant one-parameter deformations of associative algebras ⋮ Cohomology of the triangular algebra and applications. ⋮ Diagrams of Lie algebras. ⋮ Deformation Theory of Modules ⋮ Deformation of Leibniz Algebra Morphisms Over Commutative Local Algebra Base ⋮ Equivariant associative dialgebras and its one-parameter formal deformations

Cites Work

• Simplicial cohomology is Hochschild cohomology
• The cohomology structure of an associative ring
• Sur quelques points d'algèbre homologique
• On the cohomology groups of an associative algebra
• On the Deformation of Algebra Morphisms and Diagrams
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