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TRIPLE COHOMOLOGY AND DIVIDED POWERS ALGEBRAS IN PRIME CHARACTERISTIC

Part of: Homological algebra Categories and theories

Published online by Cambridge University Press:  09 October 2009

IOANNIS DOKAS
IOANNIS DOKAS*
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, PO Box 20537, CY-1678, Nicosia, Cyprus (email: dokas@ucy.ac.cy)
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Abstract

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In this paper using the Quillen–Barr–Beck (co-)homology theory of universal algebras we define (co-)homology groups for commutative algebras with divided powers in prime characteristic. In particular, we determine for A a commutative 𝔽p-algebra with divided powers, the category of Beck A-modules and the group of Beck derivations. We construct the abelianization functor and we define (co-)homology. Moreover, we determine the cohomology in low dimensions and we interpret the first cohomology in terms of extensions.

Keywords

commutative algebras with divided powersQuillen–Barr–Beck cohomologytriples

MSC classification

Secondary: 18C15: Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples 18G60: Other (co)homology theories

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 161 - 173
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

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