Poincaré duality for - Lie superalgebras
Poincaré’s proof of the co-called Birkhoff-Witt theorem
A methodical analysis of the research related to the article, “Sur les groupes continus”, of Henri Poincaré reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this article confirms the priority of his discovery of many important concepts, especially that of the universal enveloping algebra of a Lie algebra over the real or complex field, and the canonical map (symmetrization) of the symmetric algebra onto the universal enveloping...
Point modules over Sklyanin algebras.
Poisson algebras of spinor functions.
Poisson cohomology and quantization.
Poisson Lie groups and their relations to quantum groups
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
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
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.
Positive projections and Jordan structure in operator algebras.
Positivity of the -system cluster algebra.
Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
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 and and their relative invariants.
Prescribed Gauss decompositions for Kac-Moody groups over fields