Almost hermitian geometry on six dimensional nilmanifolds
Almost-graded central extensions of Lax operator algebras
Lax operator algebras constitute a new class of infinite dimensional Lie algebras of geometric origin. More precisely, they are algebras of matrices whose entries are meromorphic functions on a compact Riemann surface. They generalize classical current algebras and current algebras of Krichever-Novikov type. Lax operators for 𝔤𝔩(n), with the spectral parameter on a Riemann surface, were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structure was revealed and...
Amalgams of Weyl algebras and the ... (V, ...) conjecture.
An Algebraic Construction of a Class of Representations of a Semi-Simple Lie Algebra.
An algebraic proof of the PRV conjecture for very regular weights.
An algebraic theory of order
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...
An algorithm for analysis of the structure of finitely presented Lie algebras.
An algorithm that carries a square matrix into its transpose by an involutory congruence transformation.
An almost-integral universal Vassiliev invariant of knots.
An Analogue of the Classical Yang-Baxter Equation for General Algebraic Structures.
An analogue of the Weil representation for G2.
An elementary approach to the hypergeometric shift operators of Opdam.
An equivalence between categories of modules for generalized Kac-Moody Lie algebras.
An Equivalence of Fusion Categories.
An extension of Mahler's theorem to simply connected nilpotent groups
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras
We prove an extension of Rais' theorem on the coadjoint representation of certain graded Lie algebras. As an application, we prove that, for the coadjoint representation of any seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic stabiliser and the field of invariants is rational. It is also shown that if the highest root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra whose coadjoint representation do not...
An homotopy formula for the Hochschild cohomology
An idempotent for a Jordanian quantum complex sphere
A new Jordanian quantum complex 4-sphere together with an instanton-type idempotent is obtained as a suspension of the Jordanian quantum group .
An imprimitivity theorem for Hopf algebras.
An improvement of a result of I. N. Stewart