scholarly journals Quantum Orbit Method in the Presence of Symmetries

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 724
Author(s):  
Nicola Ciccoli
Keyword(s):  
Lie Groups ◽  
Poisson Structure ◽  
Homogeneous Spaces ◽  
Orbit Method ◽  
C Algebra ◽  
Poisson Lie Groups ◽  
Poisson Homogeneous Spaces

We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C∗-algebra quantization obtained through groupoid techniques, and we try to put the results obtained in algebraic or representation theoretical contexts in relation with groupoid quantization.

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

scholarly journals Lie-Poisson structure on some Poisson Lie groups

1992 ◽  
Vol 5 (2) ◽  
pp. 445-445 ◽  
Author(s):  
Viktor L. Ginzburg ◽  
Alan Weinstein
Keyword(s):  
Lie Groups ◽  
Poisson Structure ◽  
Poisson Lie Groups

The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

2006 ◽  
Vol 84 (10) ◽  
pp. 891-904
Author(s):  
J R Schmidt
Keyword(s):  
Coordinate System ◽  
Lie Groups ◽  
Lie Algebra ◽  
Poisson Structure ◽  
Kähler Manifolds ◽  
Coadjoint Orbits ◽  
Kahler Manifolds ◽  
Canonical Transformations ◽  
Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

scholarly journals AdS Poisson homogeneous spaces and Drinfel’d doubles

2017 ◽  
Vol 50 (39) ◽  
pp. 395202 ◽  
Author(s):  
Angel Ballesteros ◽  
Catherine Meusburger ◽  
Pedro Naranjo
Keyword(s):  
Homogeneous Spaces ◽  
Poisson Homogeneous Spaces ◽  
Drinfel'd Doubles

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

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