Abstract
In this paper, we study a tower {A n G: n} ≥ 1 of finite-dimensional algebras; here, G represents an arbitrary finite group,d denotes a complex parameter, and the algebraA n G(d) has a basis indexed by ‘G-stable equivalence relations’ on a set whereG acts freely and has 2n orbits. We show that the algebraA n G(d) is semi-simple for all but a finite set of values ofd, 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 n G(d): n} ≥ 1 (in the generic case).
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Kodiyalam, V., Srinivasan, R. & Sunder, V.S. The algebra ofG-relations. Proc Math Sci 110, 263–292 (2000). https://doi.org/10.1007/BF02878683
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DOI: https://doi.org/10.1007/BF02878683