SIMPLE CROSSED PRODUCTS OF ＄C^{*}＄ -ALGEBRAS BY LOCALLY COMPACT ABELIAN GROUPS
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概要
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"We introduce a new invariant ＄￥tilde{￥Gamma}(￥alpha)＄ , a closed subsemigroup of the dual of ＄G＄, of a ＄c*＄-dynamical system ＄(￥mathfrak{a}, G, ￥alpha)＄ where ＄￥mathfrak{a}＄ is a ＄C^{*}＄-algebra, and ＄G＄ is a locally compact abelian group with an action ＄￥alpha＄ on ＄￥mathfrak{a}＄ . We show that the crossed product ＄a￥times.G＄ is simple if and only if ＄￥mathfrak{a}＄ is ＄￥alpha＄-simple (i.e. ＄￥mathfrak{a}＄ does not have any non-trivial a-invariant ideals) and ＄￥tilde{￥Gamma}(￥alpha)＄ equals the dual of ＄G＄. We discuss some cases where ＄￥tilde{￥Gamma}(￥alpha)＄ coincides with the Connes spectrum ＄￥Gamma(￥alpha)＄ . Finally we give examples of simple crossed products of Cuntz algebras by locally compact abelian groups."
- Yokohama City Universityの論文
- 1980-00-00
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