Limit algebras of differential forms in non-commutative geometry

Bhatt, S. J. ; Inoue, A. (2008) Limit algebras of differential forms in non-commutative geometry Proceedings Mathematical Sciences, 118 (3). pp. 425-441. ISSN 0253-4142

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Given a C*-normed algebra A which is either a Banach *-algebra or a Frechet *-algebra, we study the algebras Ω A and Ω A obtained by taking respectively the projective limit and the inductive limit of Banach *-algebras obtained by completing the universal graded differential algebra Ω*A of abstract non-commutative differential forms over A. Various quantized integrals on ΩA induced by a K-cycle on A are considered. The GNS-representation of ΩA 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 Ω*A. This supplements the representation A on the space of forms discussed by Connes.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Frechet*-algebra; Graded Differential Algebra; Non-commutative Differential Forms; Quantized Integrals; K-cycle; GNS Representation
ID Code:59677
Deposited On:07 Sep 2011 05:21
Last Modified:18 May 2016 10:09

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