A property of the ideals of finite codimension of the Lie algebras of vector fields. (Une propriété des idéaux de codimension finie des algèbres de Lie de champs de vecteurs.)
À propos du calcul différentiel sur les groupes quantiques
A -analogue of the centralizer construction and skew representations of the quantum affine algebra.
A real analog of Kostant's version of the Bott-Borel-Weil theorem.
A refinement of the PRV conjecture.
A remark on a theorem of R. S. Irving and L. W. Small. (Une remarque sur un théorème de R. S. Irving et L. W. Small.)
A remark on differential operator algebras and an equivalence of categories
A remark on growth relation.
A remarkable contraction of semisimple Lie algebras
Recently, E.Feigin introduced a very interesting contraction of a semisimple Lie algebra (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of . For instance, the algebras of invariants of both adjoint and coadjoint representations of are free, and also the enveloping algebra of is a free module over its centre.
A review of Lie superalgebra cohomology for pseudoforms
This note is based on a short talk presented at the “42nd Winter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to...
A review on δ-structurable algebras
In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.
A rigidity phenomenon for germs of actions of
We study germs of Lie algebras generated by two commuting vector fields in manifolds that are maximal in the sense of Palais (those which do not present any evident obstruction to be the local model of an action of ). We study three particular pairs of homogeneous quadratic commuting vector fields (in , and ) and study the maximal Lie algebras generated by commuting vector fields whose 2-jets at the origin are the given homogeneous ones. In the first case we prove that the quadratic algebra...
A saturation property for powers of irreducible characters.
A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices
A special type of triangulations in numerical nonlinear analysis.
To calculate the zeros of a map f : Rn → Rn we consider the class of triangulations of Rn so that a certain point belongs to a simplex of fixed diameter and dimension. In this paper two types of this new class of triangulations are constructed and shown to be useful to calculate zeros of piecewise linear approximations of f.
A surjectivity theorem for rigid highest weight modules.
A symplectic representation of
We explicitly construct a particular real form of the Lie algebra in terms of symplectic matrices over the octonions, thus justifying the identifications and, at the group level, . Along the way, we provide a geometric description of the minimal representation of in terms of rank 3 objects called cubies.
A trace formula for semi-simple Lie algebras
A Transversality property of a derivation of the universal enverloping algebra U (k), for SO (n,1) and SU (n,1).
A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux.