A class of quadratic matrix algebras arising from the quantized enveloping algebra ${\s U}_q(A_{2n-1})$

Details A class of quadratic matrix algebras arising from the quantized enveloping algebra ${\s U}_q(A_{2n-1})$ A class of quadratic matrix algebras arising from the quantized enveloping algebra ${\s U}_q(A_{2n-1})$

1999-02-24

arxiv.org/abs/math/9902143v1

Mathematics

Quantum Algebra

29 pages LaTeX2e manuscript

Scientific paper

A natural family of quantized matrix algebras is introduced. It includes the two best studied such. Located inside ${\s U}_q(A_{2n-1})$, it consists of quadratic algebras with the same Hilbert series as polynomials in $n^2$ 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 $\rank\leq r$ matrices.

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