C⁎-Basic Construction from the Conditional Expectation on the Drinfeld Double. (16th June 2019) - Xin, Qiaoling; Jiang, Lining; Cao, Tianqing
Abstract : LetD ( G ) be the Drinfeld double of a finite groupG andD ( G ; H ) be the crossed product ofC ( G ) andC H, whereH is a subgroup ofG . Then the setsD ( G ) andD ( G ; H ) can be madeC ⁎ -algebras naturally. Considering theC ⁎ -basic constructionC ⁎ 〈 D ( G ), e 〉 from the conditional expectationE ofD ( G ) ontoD ( G ; H ), one can construct a crossed productC ⁎ -algebraC ( G / H × G ) ⋊ C G, such that theC ⁎ -basic constructionC ⁎ 〈 D ( G ), e 〉 isC ⁎ -algebra isomorphic toC ( G / H × G ) ⋊ C G .