Conditions for a Module to be Injective and some Applications to Hopf Algebra Duality

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Mar 1995Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 123, page 693 (issn: 0002-9939,

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Authors: Musson, Ian M.;

doi: 10.2307/2160787 , 10.1090/s0002-9939-1995-1221727-6

Conditions for a Module to be Injective and some Applications to Hopf Algebra Duality

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Abstract

We present some simple conditions for a module to be injective in certain situations. Injective modules over bialgebras often have the additional structure of module algebras, and our results can be used to give some explicit examples. In particular, we construct such a module algebra for the quantum group O q ( SL ( 2 ) ) {O_q}({\text {SL}}(2)) . Our results can also be used to describe the Hopf algebra duals of O q ( SL ( 2 ) ) {O_q}({\text {SL}}(2)) and related Hopf algebras.

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University of Wisconsin–Oshkosh
United States

Keywords

quantum groups, Hopf algebras, Injective modules, self-injective associative rings, polynormal augmentation ideals, finite-dimensional simple modules, Quantum groups (quantized enveloping algebras) and related deformations, module algebras, Hopf duals, Hopf algebras (associative rings and algebras)

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