Bhatt, S. J. ; Inoue, A. (2008) Limit algebras of differential forms in noncommutative geometry Proceedings Mathematical Sciences, 118 (3). pp. 425441. ISSN 02534142

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Official URL: http://www.ias.ac.in/mathsci/vol118/aug2008/PM2965...
Related URL: http://dx.doi.org/10.1007/s1204400800335
Abstract
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 noncommutative differential forms over A. Various quantized integrals on Ω_{∞}A induced by a Kcycle on A are considered. The GNSrepresentation of Ω_{∞}A defined by a ddimensional noncommutative volume integral on a d ^{+}summable Kcycle 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; Noncommutative Differential Forms; Quantized Integrals; Kcycle; GNS Representation 
ID Code:  59677 
Deposited On:  07 Sep 2011 05:21 
Last Modified:  18 May 2016 10:09 
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