A free associative algebra as a free module over a Specht subalgebra.
A note on centralizers in -deformed Heisenberg algebras.
A note on flat modules
Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation
2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras. Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A! is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k {0, and z, t ∈ X is satisfied...
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Domains with linear growth.
Dually slender modules and steady rings.
Exact sequences for mixed coproduct/ tensor-product ring constructions.
To a commutative ring K, and a family of K-algebras indexed by the vertex set of a graph, we associate a K-algebra obtained by a mixture of coproduct and tensor product constructions. For this, and related constructions, we give exact sequences and deduce homological properties.
Existentially closed Leibniz algebras and an embedding theorem
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
Generalizations of the primitive element theorem.
Generators and relations for Schur algebras.
Homological Dimensions of Finitely Presented Modules.
On Finitely Generated Flat Modules II.
On Finitely Generated Flat Modules III.
On the rank of semimodules over semirings.
Periodic rings with finitely generated underlying group.
Présentation jordanienne de l'algèbre de Weyl A₂
Let k be a commutative field. For any a,b∈ k, we denote by the deformation of the 2-dimensional Weyl algebra over k associated with the Jordanian Hecke symmetry with parameters a and b. We prove that: (i) any can be embedded in the usual Weyl algebra A₂(k), and (ii) is isomorphic to A₂(k) if and only if a = b.
Skew polynomial rings satisfying - property.
Some remarks on the Akivis algebras and the Pre-Lie algebras
In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I. P. Shestakov’s result that any Akivis algebra is linear and D. Segal’s result that the set of all good words in forms a linear basis of the free Pre-Lie algebra generated by the set . For completeness,...
The representation theory and the branching graph for the family of Turaev algebras .