... Page 8. 8 Anton Yu. Alekseev and Volker Schomerus In the following we make several additional... more ... Page 8. 8 Anton Yu. Alekseev and Volker Schomerus In the following we make several additional assumptions about the ribbon Hopf algebra G. To begin with, we will assume that G is semisimple. More restrictions will be imposed in subsection 3.4. ...
We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian gr... more We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian group actions with group valued moment maps. The theory is illustrated by applications to moduli spaces of flat connections on 2-manifolds.
... Anton Alekseev · Masha Podkopaeva · Pavol Ševera ... Similarly, by putting xi, j = ln(Xi, j )... more ... Anton Alekseev · Masha Podkopaeva · Pavol Ševera ... Similarly, by putting xi, j = ln(Xi, j ), one obtains the (filtered) Lie algebra pbn(K) with generators xi, j for 1 ≤ i < j ≤ n. The associated graded Lie algebra is the Lie algebra tn(K) of infinitesimal braids with generators ti, j = tj,i for ...
Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantizati... more Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product.
Journal of Differential Geometry - J DIFFEREN GEOM, 2000
A Lie group G in a group pair (D, G), integrating the Lie algebra \frak g in a Manin pair (\frak ... more A Lie group G in a group pair (D, G), integrating the Lie algebra \frak g in a Manin pair (\frak d,g), has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, and show that they generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are hamiltonian. These moment maps take values in the homogeneous space D/G. We prove an analogue of the hamiltonian reduction theorem for quasi-Poisson group actions, and we study the symplectic leaves of the orbit spaces of hamiltonian quasi-Poisson spaces.
... Page 8. 8 Anton Yu. Alekseev and Volker Schomerus In the following we make several additional... more ... Page 8. 8 Anton Yu. Alekseev and Volker Schomerus In the following we make several additional assumptions about the ribbon Hopf algebra G. To begin with, we will assume that G is semisimple. More restrictions will be imposed in subsection 3.4. ...
We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian gr... more We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian group actions with group valued moment maps. The theory is illustrated by applications to moduli spaces of flat connections on 2-manifolds.
... Anton Alekseev · Masha Podkopaeva · Pavol Ševera ... Similarly, by putting xi, j = ln(Xi, j )... more ... Anton Alekseev · Masha Podkopaeva · Pavol Ševera ... Similarly, by putting xi, j = ln(Xi, j ), one obtains the (filtered) Lie algebra pbn(K) with generators xi, j for 1 ≤ i < j ≤ n. The associated graded Lie algebra is the Lie algebra tn(K) of infinitesimal braids with generators ti, j = tj,i for ...
Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantizati... more Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product.
Journal of Differential Geometry - J DIFFEREN GEOM, 2000
A Lie group G in a group pair (D, G), integrating the Lie algebra \frak g in a Manin pair (\frak ... more A Lie group G in a group pair (D, G), integrating the Lie algebra \frak g in a Manin pair (\frak d,g), has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, and show that they generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are hamiltonian. These moment maps take values in the homogeneous space D/G. We prove an analogue of the hamiltonian reduction theorem for quasi-Poisson group actions, and we study the symplectic leaves of the orbit spaces of hamiltonian quasi-Poisson spaces.
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