On the classification of Moore algebras and their deformations.
On the deformation theory of finite dimensional algebras.
On the deformation theory of structure constants for associative algebras.
Poisson-Lie groupoids and the contraction procedure
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these...
Quantization of the Marsden-Weinstein reduction for extended Dynkin quivers
Remarks on Banach- -algebras. (Remarques sur les -algèbres de Banach.)
Remarques sur le caractère algébrique du procédé pseudo-différentiel et de certaines de ses extensions (I)
Rigid monomial algebras.
Spinors in braided geometry
Let V be a ℂ-space, be a pre-braid operator and let This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra . If and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...
Sur l'algèbre de Poisson des symboles d'une algèbre de polynômes
Sur une algèbre Q-symétrique
We establish several properties of a quadratic algebra over a field k, which is a deformation of the symmetric algebra Sk³. In particular, we prove that A is an integral domain, noetherian and Koszul; we compute its first Hochschild cohomology group; we determine the corresponding Poisson structure on k³ and its symplectic leaves; we define an involution on A and describe the corresponding irreducible involutive representations.
Symmetries in connected graded algebras and their PBW-deformations
We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo’s quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a algebra which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra , and explicitly construct all the (self-)symmetric and sign-(self-)symmetric...
Жесткость минимальных алгебр
О деформациях в многообразиях ассоциативных алгебр