Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings

Details Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings

2011-07-14

arxiv.org/abs/1107.2760v1

Mathematics

Quantum Algebra

29 pg

Scientific paper

We describe the Poisson ideals and attached symplectic geometry of a cluster
algebra with compatible Poisson structure. We apply these results to determine
the spectrum of a quantum cluster algebra. As an application, we describe the
topology on the spectra of quantized coordinate rings such as quantum matrices
and the quantized function algebra of the general linear group.

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