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This article is cited in 3 scientific papers (total in 3 papers)
Coinvariants for a coadjoint action of quantum matrices
V. V. Antonova, A. N. Zubkovb a Omsk, RUSSIA
b Chair of Geometry, Omsk State Pedagogical University, Omsk, RUSSIA
Abstract:
Let $K$ be a (algebraically closed) field. A morphism $A\mapsto g^{-1}Ag$, where $A\in M(n)$ and $g\in GL(n)$, defines an action of a general linear group $GL(n)$ on an $n\times n$-matrix space $M(n)$, referred to as an adjoint action. In correspondence with the adjoint action is the coaction $\alpha\colon K[M(n)]\to K[M(n)]\otimes K[GL(n)]$ of a Hopf algebra $K[GL(n)]$ on a coordinate algebra $K[M(n)]$ of an $n\times n$-matrix space, dual to the conjugation morphism. Such is called an adjoint coaction.
We give coinvariants of an adjoint coaction for the case where $K$ is a field of arbitrary characteristic and one of the following conditions is satisfied: (1) $q$ is not a root of unity; (2) $\operatorname{char}K=0$ and $q=\pm1$; (3) $q$ is a primitive root of unity of odd degree. Also it is shown that under the conditions specified, the category of rational $GL_q\times GL_q$-modules is a highest weight category.
Keywords:
field, adjoint action, adjoint coaction, rational module.
Received: 28.12.2008 Revised: 03.03.2009
Citation:
V. V. Antonov, A. N. Zubkov, “Coinvariants for a coadjoint action of quantum matrices”, Algebra Logika, 48:4 (2009), 425–442; Algebra and Logic, 48:4 (2009), 239–249
Linking options:
https://www.mathnet.ru/eng/al407 https://www.mathnet.ru/eng/al/v48/i4/p425
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