On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries

Details On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries

2003-05-08

arxiv.org/abs/math/0305116v1

Mathematics

Quantum Algebra

8 pages, to appear in Int. Math. Res. Notices

Scientific paper

Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry $R$ there associates a quadratic algebra which can be interpreted as the function algebra upon a certain quantum space. This paper investigates the Poincare series of this quadratic algebra. We showthat it is a rational function with numerator and denominator being a reciprocal polynomial and a skew-reciprocal polynomial, respectively.

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