Restricted Lie algebras with bounded cohomology and related classes of algebras (Q1191467)

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.