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

Abstract

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.