(Co)Homology theories for oriented algebras

Details (Co)Homology theories for oriented algebras (Co)Homology theories for oriented algebras

2006-07-05

arxiv.org/abs/math/0607141v3

Mathematics

Rings and Algebras

27 pages, 3 postscript figures. Minor changes. To appear in Comm. Algebra

Scientific paper

We study three different (co)homology theories for a family of pullbacks of algebras that we call oriented. We obtain a Mayer Vietoris long exact sequence of Hochschild and cyclic homology and cohomology groups for these algebras. We give examples showing that our sequence for Hochschild cohomology groups is different from the known ones. In case the algebras are given by quiver and relations, and that the simplicial homology and cohomology groups are defined, we obtain a similar result in a slightly wider context. Finally we also study the fundamental groups of the bound quivers involved in the pullbacks.

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