The Jucys-Murphy basis and semisimplicty criteria for the $q$-Brauer algebra

Published 27 Nov 2022 in math.RT and math.QA | (2211.14756v1)

Abstract: We construct the Jucys-Murphy elements and the Jucys-Murphy basis for the $q$-Brauer algebra in the sense of Mathas[11]. We also give a necessary and sufficient condition for the $q$-Brauer algebra being (split) semisimple over an arbitrary field.

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