Block algebras with HH1 a simple Lie algebra
| Autor: | Linckelmann, Markus, Degrassi, Lleonard Rubio y |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that if $B$ is a block of a finite group algebra $kG$ over an algebraically closed field $k$ of prime characteristic $p$ such that $\HH^1(B)$ is a simple Lie algebra and such that $B$ has a unique isomorphism class of simple modules, then $B$ is nilpotent with an elementary abelian defect group $P$ of order at least $3$, and $\HH^1(B)$ is in that case isomorphic to the Jacobson-Witt algebra $\HH^1(kP)$. In particular, no other simple modular Lie algebras arise as $\HH^1(B)$ of a block $B$ with a single isomorphism class of simple modules. Comment: 5 pages |
| Databáze: | arXiv |
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