## 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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### References:

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