poisson lie groups
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Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1324
Author(s):  
Catherine Meusburger

We review Poisson–Lie groups and their applications in gauge theory and integrable systems from a mathematical physics perspective. We also comment on recent results and developments and their applications. In particular, we discuss the role of quasitriangular Poisson–Lie groups and dynamical r-matrices in the description of moduli spaces of flat connections and the Chern–Simons gauge theory.


Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 946
Author(s):  
Michele Arzano ◽  
Jerzy Kowalski-Glikman

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After a review of the κ-Poincaré algebra, we illustrate the construction of the κ-deformed phase space of a classical relativistic particle using the tools of Lie bi-algebras and Poisson–Lie groups. We then discuss how to construct a free scalar field theory on the non-commutative κ-Minkowski space associated to the κ-Poincaré and illustrate how the group valued nature of momenta affects the field propagation.


Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 724
Author(s):  
Nicola Ciccoli

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.


2020 ◽  
pp. 225-247
Author(s):  
Brahim Alioune ◽  
Mohamed Boucetta ◽  
Ahmed Sid’Ahmed Lessiad

2017 ◽  
Vol 190 (1) ◽  
pp. 1-17 ◽  
Author(s):  
J. Abedi-Fardad ◽  
A. Rezaei-Aghdam ◽  
Gh. Haghighatdoost

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