A Note on the Bidual of a JB-Algebra.
A note on the lattice definability of Bernstein algebras.
A note on the number of generators of a nodal algebra
A pair of Jordan triple systems of Jordan pair type.
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 .)
A proof of the Russo-Dye theorem for -algebras.
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.