Kodiyalam, Vijay ; Srinivasan, R. ; Sunder, V. S. (2000) The algebra of Grelations Proceedings of the Indian Academy of Sciences  Mathematical Sciences, 110 (3). pp. 263292. ISSN 02534142

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Official URL: http://www.ias.ac.in/mathsci/vol110/aug2000/Pm1775...
Abstract
In this paper, we study a tower {A^{G}_{n}(d):n≥1} of finitedimensional algebras; here, G represents an arbitrary finite group, d denotes a complex parameter, and the algebra A^{G}_{n} (d) has a basis indexed by 'Gstable equivalence relations' on a set where G acts freely and has n orbits. We show that the algebra A^{G}_{n} (d) is semisimple for all but a finite set of values of d, and determine the representation theory (or, equivalently, the decomposition into simple summands) of this algebra in the 'generic case'. Finally we determine the Bratteli diagram of the tower {A^{G}_{n}(d):n≥1} (in the generic case).
Item Type:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Equivalence Relations; Bratteli Diagrams; Grelations; 
ID Code:  53558 
Deposited On:  09 Aug 2011 11:51 
Last Modified:  18 May 2016 06:38 
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