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- W2034211578 abstract "A finite group G is of central type (in the non-classical sense) if it admits a non-degenerate cohomology class [c] ∈ H 2(G, ℂ*) (G acts trivially on ℂ*). Groups of central type play a fundamental role in the classification of semisimple triangular complex Hopf algebras and can be determined by their representation-theoretical properties. Suppose that a finite group Q acts on an abelian group A so that there exists a bijective 1-cocycle π ∈ Z 1(Q,Ǎ), where Ǎ = Hom(A, ℂ*) is endowed with the diagonal Q-action. Under this assumption, Etingof and Gelaki gave an explicit formula for a non-degenerate 2-cocycle in Z 2(G, ℂ*), where G:= A × Q. Hence, the semidirect product G is of central type. In this paper, we present a more general correspondence between bijective and non-degenerate cohomology classes. In particular, given a bijective class [π] ∈ H 1(Q,Ǎ) as above, we construct non-degenerate classes [cπ] ∈ H 2(G,ℂ*) for certain extensions 1 → A → G → Q → 1 which are not necessarily split. We thus strictly extend the above family of central type groups." @default.
- W2034211578 created "2016-06-24" @default.
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- W2034211578 date "2009-07-01" @default.
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- W2034211578 title "On groups of central type, non-degenerate and bijective cohomology classes" @default.
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- W2034211578 doi "https://doi.org/10.1007/s11856-009-0075-0" @default.
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