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Conjugation Coinvariants of Quantum Matrices
Author(s) -
Domokos M.,
Lenagan T. H.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001650
Subject(s) - hopf algebra , commutative property , mathematics , quantum , quantum group , pure mathematics , mathematical physics , algebra over a field , quantum mechanics , physics
A quantum deformation of the classical conjugation action of GL( N , C) on the space of N × N matrices M ( N , C) is defined via a coaction of the quantum general linear group O (GL q ( N , C)) on the algebra of quantum matrices O ( M q ( N , C)). The coinvariants of this coaction are calculated. In particular, interesting commutative subalgebras of O ( M q ( N , C)) generated by (weighted) sums of principal quantum minors are obtained. For general Hopf algebras, co‐commutative elements are characterized as coinvariants with respect to a version of the adjoint coaction.