Related papers: Generalized Amitsur-Levitski theorem and equations…

In this paper we study finite W-algebras for basic classical superalgebras and Q(n) associated to the regular even nilpotent coadjoint orbits. We prove that this algebra satisfies the Amitsur-Levitzki identity and therefore all its…

In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…

We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.

A Leavitt labelled path algebra over a commutative unital ring is associated with a labelled space, generalizing Leavitt path algebras associated with graphs and ultragraphs as well as torsion-free commutative algebras generated by…

We recover results by Ullmo-Yafaev and Peterzil-Starchenko on the closure of the image of an algebraic variety in a compact complex torus. Our approach uses directed closed currents and allows us to extend the result for dimension 1 flows…

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products…

All coboundary Lie bialgebras and their corresponding Poisson--Lie structures are constructed for the oscillator algebra generated by $\{\aa,\ap,\am,\bb\}$. Quantum oscillator algebras are derived from these bialgebras by using the…

In the paper, we generalize some congruences of Lehmer for general composite numbers.

In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields…

We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.

We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations…

Kelly's combinatorial lemma is a basic tool in the study of Ulam's reconstruction conjecture. A generalization in terms of a family of t-elements subsets of a v-element set was given by Pouzet. We consider a version of this generalization…

Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely…

The author investigates the general Lie algebra of operators of coordinates, momenta, and Lorentz group generators, which can be used in quantum gravity, theories with generalized uncertainty principle, double and triple relativity and…

We introduce higher-order (or multibracket) simple Lie algebras that generalize the ordinary Lie algebras. Their `structure constants' are given by Lie algebra cohomology cocycles which, by virtue of being such, satisfy a suitable…

We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type A_{n-1}, we rederive the description of the generalized exponents in terms…

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using…

We present a realisation of the universal/simple Bershadsky--Polyakov vertex algebras as subalgebras of the tensor product of the universal/simple Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This generalises the…