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Traces and idempotents in group algebras

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Let G be a group and E an idempotent matrix with entries in the complex group algebra C G. In this paper, we study arithmetic properties of the coefficients r E (g), gG, of the Hattori-Stallings rank r E of E. Bass proved in [2] that the r E (g)’s are algebraic numbers. Following Zaleskii, we proceed by reduction to positive characteristic and give an alternative proof of that assertion, while obtaining at the same time an upper bound for the degree of the minimum polynomial of r E (g) over Q.

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  1. Department of Mathematics, University of Athens, Athens, 15784, Greece

    Ioannis Emmanouil

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  1. Ioannis Emmanouil
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Correspondence to Ioannis Emmanouil.

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Emmanouil, I. Traces and idempotents in group algebras. Math. Z. 245, 293–307 (2003). https://doi.org/10.1007/s00209-003-0543-x

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  • DOI: https://doi.org/10.1007/s00209-003-0543-x

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