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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Schur's double centralizer theorem for triangular Hopf algebras


Authors: Miriam Cohen, Davida Fischman and Sara Westreich
Journal: Proc. Amer. Math. Soc. 122 (1994), 19-29
MSC: Primary 16W30; Secondary 20C30
DOI: https://doi.org/10.1090/S0002-9939-1994-1209096-8
MathSciNet review: 1209096
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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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DOI: https://doi.org/10.1090/S0002-9939-1994-1209096-8
Article copyright: © Copyright 1994 American Mathematical Society