Abstract
The Burnside algebra for a finite inverse semigroup over a field is considered (the analog of the Grothendieck algebra). The conditions for the algebra to be Frobenius are investigated. It is shown that, if all the subgroups in the semigroup are commutative, then its Burnside algebra is Frobenius if and only if the order of any maximal subgroup is not divisible by the square of the field characteristic.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 41–52, 1974.
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Lie, I. Burnside algebra of a finite inverse semigroup. J Math Sci 9, 322–331 (1978). https://doi.org/10.1007/BF01085050
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DOI: https://doi.org/10.1007/BF01085050