(Co)Homology Theories for Oriented Algebras

DOI10.1080/00927870802089892zbMath1211.16008arXivmath/0607141OpenAlexW2135133240MaRDI QIDQ3638407

Julie Dionne, Juan Carlos Bustamante, David Smith

Publication date: 2 July 2009

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

Full work available at URL: https://arxiv.org/abs/math/0607141

zbMATH Keywords

Hochschild cohomologycyclic homologyHochschild homologyfundamental groupspullbackscyclic cohomologysimplicial homologysimplicial cohomologyMayer-Vietoris sequencesoriented algebras

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Representations of quivers and partially ordered sets (16G20)

Cites Work

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• The universal cover of a quiver with relations
• Covering spaces in representation-theory
• Finite dimensional algebras with vanishing Hochschild cohomology
• Comparing the simplicial and the Hochschild cohomologies of a finite dimensional algebra
• Hochschild cohomology of triangular matrix algebras
• Cohomology of the triangular algebra and applications.
• Cohomology of incidence algebras and simplicial complexes
• The classifying space of a bound quiver.
• The cohomology structure of an associative ring
• Nakayama oriented pullbacks and stably hereditary algebras.
• Auslander algebras Of finite representation type
• The Hochschild Cohomology Ring of a One Point Extension
• The strong no loop conjecture for special biserial algebras
• The fundamental groups of a triangular algebra
• Two non-vanishing theorems of special values of \(L\)-functions

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