A Littlewood-Richardson rule for evaluation representations of .
A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras.
A Multiplicity One Theorem for Holomorphically Induced Representations.
A natural graded Lie algebra sheaf over Riemann surfaces
A new approach to Hom-left-symmetric bialgebras
The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that -matrix is a solution of the Hom--equation by a cocycle condition.
A new Family of Irreducible, Integrable Modules for Affine Lie Algebras.
A nilpotent ideal in the Lie rings with automorphism of prime order.
A non-abelian tensor product of Leibniz algebra
Leibniz algebras are a non-commutative version of usual Lie algebras. We introduce a notion of (pre)crossed Leibniz algebra which is a simultaneous generalization of notions of representation and two-sided ideal of a Leibniz algebra. We construct the Leibniz algebra of biderivations on crossed Leibniz algebras and we define a non-abelian tensor product of Leibniz algebras. These two notions are adjoint to each other. A (co)homological characterization of these new algebraic objects enables us to...
A note on 2-step subideals of Lie algebras
A note on automorphism group of an n-generator nilpotent lie algebra
A note on coalgebra gauge theory
A generalisation of quantum principal bundles in which a quantum structure group is replaced by a coalgebra is proposed.
A note on groups with torsion-free abelianization and trivial multiplicator.
A note on parabolic subgroups.
A note on Poisson derivations
Free Poisson algebras are very closely connected with polynomial algebras, and the Poisson brackets are used to solve many problems in affine algebraic geometry. In this note, we study Poisson derivations on the symplectic Poisson algebra, and give a connection between the Jacobian conjecture with derivations on the symplectic Poisson algebra.
A note on Poisson-Lie algebroids. I.
A note on semidirect sum of Lie algebras
In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.
A particular solution of a Painlevé system in terms of the hypergeometric function .
A periodisation of semisimple Lie algebras.
A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko’s theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
A primitive ideal of contracting to a primitive ideal of . (Un idéal primitif de se contracte en un idéal primitif de .)