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Algebra i logika, 2009, Volume 48, Number 4, Pages 425–442 (Mi al407)  

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
Full-text PDF (226 kB) Citations (3)
References:
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
English version:
Algebra and Logic, 2009, Volume 48, Issue 4, Pages 239–249
DOI: https://doi.org/10.1007/s10469-009-9060-2
Bibliographic databases:
UDC: 512.55
Language: Russian
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
Citation in format AMSBIB
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\by V.~V.~Antonov, A.~N.~Zubkov
\paper Coinvariants for a~coadjoint action of quantum matrices
\jour Algebra Logika
\yr 2009
\vol 48
\issue 4
\pages 425--442
\mathnet{http://mi.mathnet.ru/al407}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2584278}
\transl
\jour Algebra and Logic
\yr 2009
\vol 48
\issue 4
\pages 239--249
\crossref{https://doi.org/10.1007/s10469-009-9060-2}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350702537}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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