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Smash products for \(G\)-sets, Clifford theory and duality theorems. (English) Zbl 0836.16029
Motivated by the study of Clifford theory and duality theorems, the authors develop the theory of smash products for \(G\)-sets, where \(G\) is a group. They extend E. Dade’s graded Clifford theory [J. Reine Angew. Math. 369, 40-86 (1986; Zbl 0583.16001)] to the case of \(G\)-set gradations and they also obtain a duality theorem which extends a result of M. Beattie [J. Algebra 115, 303-312 (1988; Zbl 0647.16010)].
MSC:
16W50 Graded rings and modules (associative rings and algebras)
16S40 Smash products of general Hopf actions
16D90 Module categories in associative algebras
16W20 Automorphisms and endomorphisms
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