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

  • Subhash J. Bhatt
Regular Articles

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.

Keywords

Frechet*-algebra enveloping Σ-C*-algebra smooth crossed product m-tempered action K-theory differential structure inC*-algebras 

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Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  1. 1.Department of MathematicsSardar Patel UniversityVallabh VidyanagarIndia

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