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Restricted Lie algebras with bounded cohomology and related classes of algebras. (English) Zbl 0756.17008

The finite-dimensional Lie \(p\)-algebras \(L\) with bounded Hochschild cohomology (i.e.
\(\dim H^ n_ *(L,M)<b(L,M)\) for every \(n\geq 0\)) are investigated. The equivalence of the following properties is stated: 1) \(L\) is special, 2) \(L\) is of finite module type, 3) \(L\) is of bounded module type, 4) \(L\) has periodic cohomology, 5) \(L\) has bounded cohomology. The structure of such algebras and their indecomposable \(p\)-representations are determined. In particular, all the Lie \(p\)-algebras of finite representation type are described.

MSC:

17B50 Modular Lie (super)algebras
17B56 Cohomology of Lie (super)algebras
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