Variation of complex structures and variation of Lie algebras.
Variational calculus on Lie algebroids
It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.
Variétés de drapeaux et réseaux de Toda.
Varieties of modules over tubular algebras
We classify the irreducible components of varieties of modules over tubular algebras. Our results are stated in terms of root combinatorics. They can be applied to understand the varieties of modules over the preprojective algebras of Dynkin type 𝔸₅ and 𝔻₄.
Varieties of nilpotent Lie algebras of dimension less than 8
Vecteurs différentiables dans les représentations unitaires des groupes de Lie
Vector bundles on plane cubic curves and the classical Yang–Baxter equation
In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical -matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic -matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin’s classication and prove...
Vector fields on the space of functions univalent inside the unit disk via Faber polynomials.
Vector form brackets in Lie algebroids.
Vector form brackets in Lie algebroids
A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.
Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions
We classify quadratic - and -modules by crude computation, generalising in the first case a Theorem proved independently by F.G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearisation results for abstract modules of algebraic groups and associated Lie rings.
Verma module annihilators for quantized enveloping algebras
Vertex algebras and algebraic curves
Vertex algebras and the formal loop space
We construct a certain algebro-geometric version of the free loop space for a complex algebraic variety X. This is an ind-scheme containing the scheme of formal arcs in X as studied by Kontsevich and Denef-Loeser. We describe the chiral de Rham complex of Malikov, Schechtman and Vaintrob in terms of the space of formal distributions on supported in . We also show that possesses a factorization structure: a certain non-linear version of a vertex algebra structure. This explains the heuristic...
Vertex algebroids over Veronese rings.
Vertex tensor category structure on a category of Kazhdan-Lusztig.
Výpočet polynomů Kazhdana, Lustiga a Vogana pro rozštěpení grupy