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- W2000572223 abstract "In this paper we use Quillen–Barr–Beck's theory of (co-) homology of algebras in order to define (co-) homology for the category RLie of restricted Lie algebras over a field k of characteristic p≠0. In contrast with the cases of groups, associative algebras and Lie algebras we do not obtain Hochschild (co-) homology shifted by 1. Precisely, we determine for L∈RLie the category of Beck L-modules and the group of Beck derivations of g∈RLie/L to a Beck L-module M. Moreover, we prove a classification theorem which gives a one-to-one correspondence between the one cohomology and the set of equivalent classes of p-extensions. Finally, a universal coefficient theorem is proved, relating the homology to the Hochschild homology via a short exact sequence. This shows that the new homology determines the Hochschild homology." @default.
- W2000572223 created "2016-06-24" @default.
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- W2000572223 date "2004-01-01" @default.
- W2000572223 modified "2023-09-23" @default.
- W2000572223 title "Quillen–Barr–Beck (co-) homology for restricted Lie algebras" @default.
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- W2000572223 doi "https://doi.org/10.1016/s0022-4049(03)00120-8" @default.
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