Related papers: Iterative algebras
In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.
In this paper, by using Gr\"obner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative…
We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…
We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra, called big algebra, attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are…
According to Kirillov's theory, the construction of a unitary irreducible representation of a nilpotent Lie group requires a precise computation of some polarizing subalgebra subordinated to a linear functional in the linear dual of the…
We proved in a previous article that the bar complex of an E-infinity algebra inherits a natural E-infinity algebra structure. As a consequence, a well-defined iterated bar construction B^n(A) can be associated to any algebra over an…
To define the notion of a generic property of finite dimensional 2-step nilpotent Lie algebras we use standard correspondence between such Lie algebras and points of an appropriate algebraic variety, where a negligible set is one contained…
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra $L(\Lambda)$ generated by indecomposable constructible sets in the varieties of modules for any finite dimensional $\mathbb{C}$-algebra $\Lambda.$ We…
We consider the Lie algebra associated with the descending central series filtration of the pure braid group of a closed surface of arbitrary genus. R. Bezrukavnikov gave a presentation of this Lie algebra over the rational numbers. We show…
We present a construction of 2-step nilpotent Lie algebras using labeled directed simple graphs, which allows us to give a criterion to detect certain ideals and subalgebras by finding special subgraphs. We prove that if a label occurs only…
Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.
Smoktunowicz, Lenagan, and the second-named author recently gave an example of a nil algebra of Gelfand-Kirillov dimension at most three. Their construction requires a countable base field, however. We show that for any field $k$ and any…
We introduce the notion of $\lambda$-double Lie algebra, which coincides with usual double Lie algebra when $\lambda = 0$. We state that every $\lambda$-double Lie algebra for $\lambda\neq0$ provides the structure of modified double Poisson…
For the polynomial ring over an arbitrary field with twelve variables, there exists a prime ideal whose symbolic Rees algebra is not finitely generated.
We determine the isomorphism classes of the first family of infinite dimensional simple Lie algebras recently introduced by Xu. The structure space of these algebras is given explicitly. The derivations of these algebras are also…
We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double…
We define the notions of finite-state and functionally recursive matrices and their growth. We also introduce two rings generated by functionally recursive matrices. The first is isomorphic to the 2-generated free ring. The second is a…
We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…