English

Poisson and quantum geometry of acyclic cluster algebras

Quantum Algebra 2012-10-23 v1

Abstract

We prove that certain acyclic cluster algebras over the complex numbers are the coordinate rings of holomorphic symplectic manifolds. We also show that the corresponding quantum cluster algebras have no non-trivial prime ideals. This allows us to give evidence for a generalization of the conjectured variant of the orbit method for quantized coordinate rings and their classical limits.

Keywords

Cite

@article{arxiv.1210.5824,
  title  = {Poisson and quantum geometry of acyclic cluster algebras},
  author = {Sebastian Zwicknagl},
  journal= {arXiv preprint arXiv:1210.5824},
  year   = {2012}
}

Comments

12 pg. arXiv admin note: substantial text overlap with arXiv:1009.2936