ON THE STRUCTURE OF COHOMOLOGY RINGS OF p-NILPOTENT LIE ALGEBRAS
| Autor: | Daniel K. Nakano, Jon F. Carlson |
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| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Pure mathematics Algebra and Number Theory Mathematics::Commutative Algebra Group cohomology 010102 general mathematics Lie algebra cohomology Group Theory (math.GR) 01 natural sciences Cohomology ring Lie conformal algebra Graded Lie algebra Restricted Lie algebra 0103 physical sciences Spectral sequence FOS: Mathematics Equivariant cohomology 010307 mathematical physics Geometry and Topology Representation Theory (math.RT) 0101 mathematics Mathematics - Group Theory Mathematics - Representation Theory 20C20 Mathematics |
| Zdroj: | Transformation Groups. 19:721-734 |
| ISSN: | 1531-586X 1083-4362 |
| Popis: | In this paper the authors investigate the structure of the restricted Lie algebra cohomology of p-nilpotent Lie algebras with trivial p-power operation. Our study is facilitated by a spectral sequence whose E 2-term is the tensor product of the symmetric algebra on the dual of the Lie algebra with the ordinary Lie algebra cohomology and converges to the restricted cohomology ring. In many cases this spectral sequence collapses, and thus, the restricted Lie algebra cohomology is Cohen–Macaulay. A stronger result involves the collapsing of the spectral sequence and the cohomology ring identifying as a ring with the E 2-term. We present criteria for the collapsing of this spectral sequence and provide some examples where the ring isomorphism fails. Furthermore, we show that there are instances when the spectral sequence does not collapse and yields cohomology rings which are not Cohen-Macaulay. |
| Databáze: | OpenAIRE |
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