4 citations · 4 across the 5 of their papers we have counts for
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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…
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…
R-Matrix Poisson Algebras and Their Deformations
Sebastian Zwicknagl
We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classi…
Braided Symmetric and Exterior Algebras
Arkady Berenstein, Sebastian Zwicknagl
We introduce and study symmetric and exterior algebras in braided monoidal categories such as the category O for quantum groups. We relate our braided symmetric algebras and braide…