Factorizable Module Algebras

DOI10.1093/IMRN/RNX307zbMATH Open1473.17030arXiv1701.05798OpenAlexW2977822545MaRDI QIDQ5243463

Author name not available (Why is that?)

Publication date: 18 November 2019

Published in: (Search for Journal in Brave)

Abstract: The aim of this paper is to introduce and study a large class of

m a t h f r a k g

-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras of corresponding reductive groups

G

, their parabolic subgroups, basic affine spaces and many others. It turns out that tensor products of factorizable algebras are also factorizable and it is easy to create a factorizable algebra out of virtually any

m a t h f r a k g

-module algebra. We also have quantum versions of all these constructions in the category of

U_{q} (m a t h f r a k g)

-module algebras. Quite surprisingly, our quantum factorizable algebras are naturally acted on by the quantized enveloping algebra

U_{q} (m a t h f r a k g^{*})

of the dual Lie bialgebra

m a t h f r a k g^{*}

of

m a t h f r a k g

.

Full work available at URL: https://arxiv.org/abs/1701.05798

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