Coinvariants for a coadjoint action of quantum matrices |
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Authors: | V V Antonov A N Zubkov |
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Institution: | 1.50 let Oktyabrya, 116-17,Omsk,Russia;2.Omsk Pedagogical State University,Omsk,Russia |
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Abstract: | Let K be a (algebraically closed ) field. A morphism A ⟼ g
−1
Ag, where A ∈ M(n) and g ∈ GL(n), defines an action of a general linear group GL(n) on an n × n-matrix space M(n), referred to as an adjoint action. In correspondence with the adjoint action is the coaction α: KM(n)] → KM(n)] ⊗ KGL(n)] of a Hopf algebra KGL(n)] on a coordinate algebra KM(n)] of an n × 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) char K = 0 and q = ±1; (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
× GL
q
-modules is a highest weight category. |
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Keywords: | |
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