Coinvariants for a coadjoint action of quantum matrices

V. V. Antonov, A. N. Zubkov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let K be a (algebraically closed) field. A morphism A {long rightwards arrow from bar} g-1Ag, 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: K[M(n)] → K[M(n)] ⊗ K[GL(n)] of a Hopf algebra K[GL(n)] on a coordinate algebra K[M(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 GLq × GLq-modules is a highest weight category.

Original languageEnglish
Pages (from-to)239-249
Number of pages11
JournalAlgebra and Logic
Issue number4
Publication statusPublished - Oct 2009
Externally publishedYes


  • Adjoint action
  • Adjoint coaction
  • Field
  • Rational module

ASJC Scopus subject areas

  • Analysis
  • Logic


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