• Limit Algebras of Differential Forms in Non-Commutative Geometry

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    • Keywords

       

      Frechet ∗-algebra; graded differential algebra; non-commutative differential forms; quantized integrals; K-cycle; GNS representation.

    • Abstract

       

      Given a C∗-normed algebra A which is either a Banach ∗-algebra or a Frechet ∗-algebra, we study the algebras ∞A and A obtained by taking respectively the projective limit and the inductive limit of Banach ∗-algebras obtained by completing the universal graded differential algebra ∗A of abstract non-commutative differential forms over A. Various quantized integrals on ∞A induced by a K-cycle on A are considered. The GNS-representation of ∞A defined by a d-dimensional non-commutative volume integral on a d+-summable K-cycle on A is realized as the representation induced by the left action of A on ∗A. This supplements the representation A on the space of forms discussed by Connes (Ch. VI.1, Prop. 5, p. 550 of [C]).

    • Author Affiliations

       

      S J Bhatt1 A Inoue2

      1. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, India
      2. Department of Applied Mathematics, Fukuoka University, Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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