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Enveloping Σ-C *-algebra of a smooth Frechet algebra crossed product by ℝ,K-theory and differential structure inC *-algebras

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Abstract

Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C *-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A ∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C *-crossed productC *(ℝ,E(A), α) of the enveloping Σ-C *-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK *(S(ℝ, A∞, α)) =K *(C *(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC *-algebra defined by densely defined differential seminorms is given.

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  1. Department of Mathematics, Sardar Patel University, 388 120, Vallabh Vidyanagar, India

    Subhash J. Bhatt

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  1. Subhash J. Bhatt
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Bhatt, S.J. Enveloping Σ-C *-algebra of a smooth Frechet algebra crossed product by ℝ,K-theory and differential structure inC *-algebras. Proc. Indian Acad. Sci. (Math. Sci.) 116, 161–173 (2006). https://doi.org/10.1007/BF02829785

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