Crossed Products of Locally C-algebras
نویسنده
چکیده
The crossed products of locally C-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C-algebra is proved. 2000 AMS Mathematics subject classification. Primary 46L05, 46L55.
منابع مشابه
Full Crossed Products by Coactions,
Let δ be a coaction of a locally compact group G on a C*-algebra A. We show that if I is a δ-invariant ideal in A, then 0! I¬δ I G!A¬δ G! (A}I )¬δI G! 0 for full crossed products, as Landstad et al. have done for spatial crossed products by coactions. We prove that for suitable coactions, the crossed products of C ! (X )-algebras are again C ! (X )-algebras, and the crossed products of continuo...
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We introduce the notion of strong Morita equivalence for group actions on locally C-algebras and prove that the crossed products associated with two strongly Morita equivalent continuous inverse limit actions of a locally compact group G on the locally C∗-algebras A and B are strongly Morita equivalent. This generalizes a result of F. Combes, Proc. London Math. Soc. 49(1984) and R. E. Curto, P....
متن کاملDuality for Actions
Let G be a locally compact group. We show that the category A(G) of actions of G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma catego...
متن کاملFull Crossed Products by Hopf C∗-algebras
We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.
متن کاملCourse Description: Crossed Products of C*-algebras and Banach Algebras, University of Toronto, Spring Semester 2014
A crossed product is the functional analysts’ version of a skew group ring. Thus, if α : G→ Aut(A) is an action of a locally compact group G on a Banach algebra A, then a crossed product Banach algebra encodes the action of G on A, and its representation theory is related to pairs (u, π) consisting of a representation u of G and a representation π of A on the same Banach space such that ugπ(a)u...
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