C ? -Basic Construction from the Conditional Expectation on the Drinfeld Double

摘要

Let D(G) be the Drinfeld double of a finite group G and D(G;H) be the crossed product of C(G) and CH, where H is a subgroup of G. Then the sets D(G) and D(G;H) can be made C?-algebras naturally. Considering the C?-basic construction C??D(G),e? from the conditional expectation E of D(G) onto D(G;H), one can construct a crossed product C?-algebra C(G/H×G)?CG, such that the C?-basic construction C??D(G),e? is C?-algebra isomorphic to C(G/H×G)?CG.