The algebra of G-relations

Kodiyalam, Vijay ; Srinivasan, R. ; Sunder, V. S. (2000) The algebra of G-relations Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 110 (3). pp. 263-292. ISSN 0253-4142

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In this paper, we study a tower {AGn(d):n≥1} of finite-dimensional algebras; here, G represents an arbitrary finite group, d denotes a complex parameter, and the algebra AGn (d) has a basis indexed by 'G-stable equivalence relations' on a set where G acts freely and has n orbits. We show that the algebra AGn (d) is semi-simple 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 {AGn(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; G-relations;
ID Code:53558
Deposited On:09 Aug 2011 11:51
Last Modified:18 May 2016 06:38

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