Abstract
The graded algebra of invariant elements under the representations induced by the Yang-Baxter operators constructed in our previous work is used here to generalize the notion of minors associated to a matrix with coefficients in any -commutative algebra . We call them quantum minors to be reminded that they are obtained in a non commutative context. Quantum minors are elements of A appearing as coefficients of the algebra endomorphism induced on the graded algebra of invariant elements by a given A-module endomorphism. It turns out that quantum minors are multiplicative and satisfy a Laplace-like expansion. It is shown that the usual determinant, the various -graded determinants, and the quantum and multiparametric quantum determinants are special cases of quantum minors, depending on the choice of the commutation factor .
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