A class of quadratic matrix algebras arising from the quantized enveloping algebra Uq(A2n−1)

A natural family of quantized matrix algebras is introduced. It includes the two best studied such. Located inside Uq(A2n−1), it consists of quadratic algebras with the same Hilbert series as polynomials in n2 variables. We discuss their general properties and investigate some members of the family in great detail with respect to associated varieties, degrees, centers, and symplectic leaves. Finally, the space of rank r matrices becomes a Poisson submanifold, and there is an associated tensor category of rank ⩽r matrices.