Schur’s double centralizer theorem for triangular Hopf algebras

Cohen, Miriam; Fischman, Davida; Westreich, Sara

doi:10.1090/S0002-9939-1994-1209096-8

Schur’s double centralizer theorem for triangular Hopf algebras
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by Miriam Cohen, Davida Fischman and Sara Westreich PDF

Proc. Amer. Math. Soc. 122 (1994), 19-29 Request permission

Abstract:

Let (H, R) be a triangular Hopf algebra and let V be a finite-dimensional representation of H. Following Manin we imitate the standard algebraic constructions in order to define the relativized notions of R-universal enveloping algebras of R-Lie algebras and the R-Lie algebra ${\text {gl}_R}(V)$. Using Majid’s "bosonization" theorem and the above we prove an R-analogue of Schur’s double centralizer theorem.

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Cross products by Braided groups and Bosonization

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