ISSN:
1573-0514
Keywords:
Banach algebras
;
finite group actions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetA be a real or complex Banach algebra and assume that α is an action of a finite groupG onA by means of continuous automorphisms. To such a finite covariant system (A, G, α), we associate an Abelian groupK(A, G, α). We obtain some classical exact sequences for an algebraA and a closed invariant idealI. We also compute the group in a few important special cases. Doing so, we relate our new invariant to the classicalK 0 andK 1 of a Banach algebra and to theK-theory of ℤ2-graded Banach algebras. Finally, we obtain a result that gives a close relationship of our groupK(A, G, α) with theK-theory of the crossed productA ⨂α G. In particular, we prove a six-term exact sequence involving our groupK(A, G, α) and theK-groups ofA ⨂α G. In this way, we hope to contribute to the well-known problem of finding theK-theory of the crossed productA ⨂α G in the case of an action of a finite group.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00961340
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