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Averaging operators on $q$-deformed Witt and $q$-deformed $W(2,2)$ algebras (2304.00662v1)

Published 3 Apr 2023 in math.QA, math-ph, math.MP, and math.RA

Abstract: The aim of this paper is to give some constructions results of averaging operators on Hom-Lie algebras. The homogeneous averaging operators on $q$-deformed Witt and $q$-deformed $W(2,2)$ Hom-algebras are classified. As applications, the induced Hom-Leibniz algebra structures are obtained and their multiplicativity conditions are also given.