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In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by Prim(U(g)) the set of (graded) primitive ideals of the enveloping algebra U(g...
The aim of this paper is to describe the irregular locus of the commuting variety of a reductive symmetric Lie algebra. More precisely, we want to enlighten a remark of Popov. In [Po], the irregular l...
From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz n-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Li...
Static SKT metrics on Lie groups      Static SKT metrics  Lie groups        font style='font-size:12px;'> 2010/11/29
An SKT metric is an Hermitian metric on a complex manifold whose fundamental 2-form ! satisfies @@! = 0. Streets and Tian introduced in [STb] a Ricci-type flow that preserves the SKT condition.
Asymptotic behaviour of the Lie module     Asymptotic behaviour  ie module        font style='font-size:12px;'> 2010/11/30
We obtain a projective submodule of Lie(n) in prime char-acteristic p for n not a p-power, and show that the ratio of its dimension to that of Lie(n) approaches 1 as n tends to infinity.
Poincare Polynomial of a Kac-Moody Lie algebra can be obtained by classifying the Weyl orbit W() of its Weyl vector . A remarkable fact for Affine Lie algebras is that the number of elements of W(...
In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that ...
Representations of Affine and Toroidal Lie Algebras     Representations of Affine  Toroidal Lie Algebras       font style='font-size:12px;'> 2010/12/1
We discuss the category I of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties.
We consider finite W-algebras U(g, e) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible U(g, e)-modules with inte...
A theorem of Siebert asserts that if μn(t) are semigroups of probability measures on a Lie group G, and Pn are the corresponding generating functionals,then μn(t).
Snyder Space-Time: K-Loop and Lie Triple System     Snyder space-time  quantum group       font style='font-size:12px;'> 2010/12/13
Different deformations of the Poincar´e symmetries have been identified for various non-commutative spaces (e.g. κ-Minkowski, sl(2,R), Moyal). We present here the deformation of the Poincar&acut...
All gradings by abelian groups are classified on the following al-gebras over an algebraically closed field F: the simple Lie algebra of type G2 (char F 6= 2, 3), the exceptional simple Jordan algebra...
In this paper, a variable-coefficient Gardner equation is considered. By using the classical symmetry analysis method symmetries for this equation are obtained. Then, the generalized Jacobi elliptic f...
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restric...
Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whe...

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