4 citations · 9 across the 9 of their papers we have counts for
9 papers
Cluster Algebras, Symplectic Leaves and Quantum Groups
Sebastian Zwicknagl
This paper investigates the Poisson geometry of cluster algebras and the corresponding ideal theory of quantum cluster algebras. We then show how our approach can be applied to the…
Poisson and quantum geometry of acyclic cluster algebras
Sebastian Zwicknagl
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 cl…
Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings
Sebastian Zwicknagl
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 quantu…
Toric Poisson Ideals in Cluster Algebras
Sebastian Zwicknagl
This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumpt…
Braided Symmetric Algebras of Simple -Modules and Their Geometry
Sebastian Zwicknagl
In the present paper we prove decomposition formulae for the braided symmetric powers of simple modules over the quantized enveloping algebra ; natural quantum analogues…
Equivariant Quantizations of Symmetric Algebras
Sebastian Zwicknagl
Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quan…