Generalizing Clifford module periodicity to graded representations (Q1891696)

The author introduces graded representations in order to provide a more natural and manageable framework for the constructions and results of his previous papers. The main result (which is still too technical to be stated here) is a Morita equivalence which generalizes the periodicity equivalence [obtained in Commun. Algebra 21, No. 7, 2211-2249 (1993; Zbl 0787.20010)]. This result has applications to projective representations of monomial groups, simplifying considerably the constructions made by the author [Can. J. Math. 45, No. 2, 295-339 (1993; Zbl 0815.20012)]. Two variants of the main theorem are also given; one of them generalizes an eightfold periodicity that includes real Clifford module periodicity.