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

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/116/02/0161-0173

    • Keywords

       

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

    • 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.

    • Author Affiliations

       

      Subhash J Bhatt1

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

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.