(Co)Homology Theories for Oriented Algebras |
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Authors: | Juan Carlos Bustamante Julie Dionne |
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Institution: | 1. Departamento de Matemáticas , Universidad San Francisco de Quito , Quito, Ecuador;2. Département de Mathématiques , Université de Sherbrooke , Québec, Canada |
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Abstract: | 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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Keywords: | Cyclic (co)homology Fundamental group Hochschild (co)homology Oriented algebras Pullbacks Simplicial (co)homology |
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