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 commutativity of nonassociative rings.
A note on groups with torsion-free abelianization and trivial multiplicator.
A note on Jordan automorphisms
A note on Jordan rings of quotients
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 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