Conjugation Coinvariants of Quantum Matrices

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.