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.
A -representation with no quantum symmetric algebra
We show by explicit calculations in the particular case of the 4-dimensional irreducible representation of that it is not always possible to generalize to the quantum case the notion of symmetric algebra of a Lie algebra representation.
Abelian closure in soluble Lie rings
Abelian complex structures on 6-dimensional compact nilmanifolds
We classify the -dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure we describe the space of symplectic forms which are compatible with .
Abelian complex structures on solvable Lie algebras.
Abelian extensions of Lie bialgebras. (Extensions abéliennes des bigèbres de Lie.)
Abelian ideals of a Borel subalgebra and root systems
Let be a simple Lie algebra and the poset of non-trivial abelian ideals of a fixed Borel subalgebra of . In [8], we constructed a partition parameterised by the long positive roots of and studied the subposets . In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of is a join-semilattice.
Abelian Varieties, l-adic Representations and Lie Algebras.