Braided modules and reflection equations

Dimitri Gurevich

Displaying similar documents to “Braided modules and reflection equations”

Introduction to quantum Lie algebras

Gustav Delius (1997)

Banach Center Publications

Similarity:

Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras $U_{h} (g)$ . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of ${(s l_{2})}_{h}$ .

Comtrans algebras and their physical applications

Jonathan Smith (1993)

Banach Center Publications

Similarity:

The PBW filtration, Demazure modules and toroidal current algebras.

Feigin, Evgeny (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

The derived Lie pseudoalgebra of an anchored module.

Popescu, Paul, Popescu, Marcela (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Similarity:

Classification of the simple modules of the quantum Weyl algebra and the quantum plane

Vladimir Bavula (1997)

Banach Center Publications

Similarity:

The supports of simple modules over toroidal algebras.

Mazorchuk, Volodymyr (1999)

Journal of Lie Theory

Similarity:

$κ$ -Minkowski spacetimes and DSR algebras: fresh look and old problems.

Borowiec, Andrzej, Pachol, Anna (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Quantum probability, renormalization and infinite-dimensional *-Lie algebras.

Accardi, Luigi, Boukas, Andreas (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

On bounded generalized Harish-Chandra modules

Ivan Penkov, Vera Serganova (2012)

Annales de l’institut Fourier

Similarity:

Let $𝔤$ be a complex reductive Lie algebra and $𝔨 \subset 𝔤$ be any reductive in $𝔤$ subalgebra. We call a $(𝔤, 𝔨)$ -module $M$ bounded if the $𝔨$ -multiplicities of $M$ are uniformly bounded. In this paper we initiate a general study of simple bounded $(𝔤, 𝔨)$ -modules. We prove a strong necessary condition for a subalgebra $𝔨$ to be bounded (Corollary 4.6), to admit an infinite-dimensional simple bounded $(𝔤, 𝔨)$ -module, and then establish a sufficient condition for a subalgebra $𝔨$ to be bounded (Theorem 5.1). As a result we are...

Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations

Angel Ballesteros, Mariano del Olmo (1997)

Banach Center Publications

Similarity:

Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach. ...