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Poisson Lie groups and their relations to quantum groups

Janusz Grabowski (1995)

Banach Center Publications

The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic facts about...

Poisson-Lie groupoids and the contraction procedure

Kenny De Commer (2015)

Banach Center Publications

On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these...

Poisson-Lie groups and complete integrability. I. Drinfeld bigebras, dual extensions and their canonical representations

Y. Kosmann-Schwarzbach, F. Magri (1988)

Annales de l'I.H.P. Physique théorique

Poisson-Nijenhuis structures

Yvette Kosmann-Schwarzbach, Franco Magri (1990)

Annales de l'I.H.P. Physique théorique

Polarisation dans les algèbres de Lie. II

Jacques Dixmier (1976)

Bulletin de la Société Mathématique de France

Polarisations dans les algèbres de Lie

Jacques Dixmier (1971)

Annales scientifiques de l'École Normale Supérieure

Polarization in the Classical Groups.

Wim H. Hesselink (1978)

Mathematische Zeitschrift

Polycyclic groups, Lie algebras and algebraic groups.

Stephen Donkin (1981)

Journal für die reine und angewandte Mathematik

Polynômes de Joseph et représentation de Springer

Michèle Vergne (1990)

Annales scientifiques de l'École Normale Supérieure

Polynomial identities in smash products.

Bahturin, Yuri, Petrogradsky, Victor (2002)

Journal of Lie Theory

Positivity of the $T$ -system cluster algebra.

Di Francesco, Philippe, Kedem, Rinat (2009)

The Electronic Journal of Combinatorics [electronic only]

Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

K.K. Abdurasulov, A.Kh. Khudoyberdiyev, M. Ladra, A.M. Sattarov (2021)

Communications in Mathematics

In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent....

Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras $E_{6 (6)}$ and $E_{6 (- 26)}$ and their relative invariants.

Jackson, Steven Glenn, Noël, Alfred G. (2006)

Experimental Mathematics

Prescribed Gauss decompositions for Kac-Moody groups over fields

Jun Morita, Eugene Plotkin (2001)

Rendiconti del Seminario Matematico della Università di Padova

Primitive Ideals and Orbital Integrals in Complex Classical Groups.

Dan Barbasch, David Vogan (1982)

Mathematische Annalen

Primitive Ideals and Symplectic Leaves of Quantum Matrices

Mosin, V. G. (2000)

Serdica Mathematical Journal

It is proved that there exists a bijection between the primitive ideals of the algebra of regular functions on quantum m × n-matrices and the symplectic leaves of associated Poisson structure.

Problems in the theory of quantum groups

Shuzhou Wang (1997)

Banach Center Publications

This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.

Currently displaying 21 – 40 of 53

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Displaying 21 – 40 of 53

Poisson Lie groups and their relations to quantum groups

Poisson-Lie groupoids and the contraction procedure

Poisson-Lie groups and complete integrability. I. Drinfeld bigebras, dual extensions and their canonical representations

Poisson-Nijenhuis structures

Polarisation dans les algèbres de Lie. II

Polarisations dans les algèbres de Lie

Polarization in the Classical Groups.

Polycyclic groups, Lie algebras and algebraic groups.

Polynômes de Joseph et représentation de Springer

Polynomial identities in smash products.

Positivity of the $T$ -system cluster algebra.

Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras $E_{6 (6)}$ and $E_{6 (- 26)}$ and their relative invariants.

Prescribed Gauss decompositions for Kac-Moody groups over fields

Primitive Ideals and Orbital Integrals in Complex Classical Groups.

Primitive Ideals and Symplectic Leaves of Quantum Matrices

Problems in the theory of quantum groups

Produced representations of Lie algebras and superfields

Product formulas for modular forms on $O (2, n)$

Product structures on four dimensional solvable Lie algebras.

Currently displaying 21 – 40 of 53