Poisson-Lie T-duality and Courant algebroids
Poisson-Lie T-duality is explained using the language of Courant algebroids.
math.SG↗
arXiv subjects
Pavol Ševera
Publications and source records attributed to Pavol Ševera.
On Deformation Quantization of Poisson-Lie Groups and Moduli Spaces of Flat Connections
We give simple explicit formulas for deformation quantization of Poisson-Lie groups and of similar Poisson manifolds which can be represented as moduli spaces of flat connections on surfaces. The star products depend on a choice of Drinfeľd associator and are obtained by applying certain monoidal functors (fusion and reduction) to commutative algebras in Drinfeľd categories. From a geometric point of view this construction can be understood as a quantization of the quasi-Poisson structures on moduli spaces of flat connections.
math.QA↗
On quantization of quasi-Lie bialgebras
We modify the quantization of Etingof and Kazhdan so that it can be used to quantize quasi-Lie bialgebras.
math.QA↗
Moduli spaces of flat connections and Morita equivalence of quantum tori
We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure (such as symplectic groupoid structure) gets a geometrical explanation via 3-dimensional cobordisms. We give a formula for the symplectic form in terms of holonomies, based on a central extension of the gauge group by closed 2-forms. This construction is finally used for a certain extension of the Morita equivalence of quantum tori to the world of Poisson-Lie groups.
math.SG↗