Related papers: Two-dimensional Virasoro algebras

In this paper we show the unexpected property that extension from local to global without loss of regularity holds for the solutions of a wide class of vector-valued differential equations, in particular for the class of fractional abstract…

Let $X$ be a smooth projective complex variety and let $D=D_1+\cdots+D_l$ be a reduced normal crossing divisor on $X$ with each component $D_j$ smooth, irreducible, and nef. The log-local principle of van Garrel-Graber-Ruddat conjectures…

We consider general linear superalgebra (type A) and tensor with Laurent polynomial ring in several variables. We then consider the universal central extension of this Lie superalgebra which we call toroidal superalgebra. We give a faithful…

This paper establishes semiorthogonal decompositions for derived Grassmannians of perfect complexes with Tor-amplitude in $[0,1]$. This result verifies the author's Quot formula conjecture [J21a] and generalizes and strengthens Toda's…

In this paper the derivation algebra and automorphism group of the twisted deformative Schr\"{o}dinger-Virasoro Lie algebras are determined.

Let k be any field. J-P. Serre proved that the spectrum of the Grothendieck ring of the k-representation category of a group is connected, and that the same holds in characteristic zero for the representation category of a Lie algebra over…

The closure of a Diximier sheet is the image of a generalized Grothendieck's simultaneous resolution. We show that the associated variety of simple affine vertex algebras is contained in the closure of the Diximier sheet when a…

In this paper, we prove a window theorem for categorical Donaldson-Thomas theories on local surfaces as an analogue of window theorem for GIT quotient stacks. We give two applications of our main result. The first one is a proof of…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…

We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the analysis of a Leibniz algebra that underlies these vector…

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…

This is the integral text of my thesis. The first part is an expanded version of "Riemann-Roch theorems for Deligne-Mumford stacks", where I deal with Artin stacks over general bases. In the second part, I prove some Riemann-Roch statment…

Structures of dual Lie bialgebras on the one sided Witt algebra, the Witt algebra and the Virasoro algebra are investigated. As a result, we obtain some infinite dimensional Lie algebras.

Let X be an algebraic curve, defined over a perfect field, and G a divisor on X. If X has sufficiently many points, we show how to construct a divisor D on X such that l(2D-G)=0, of essentially any degree such that this is compatible the…

This article is the first report of an ongoing project aimed at finding a geometric interpretation of the Witten genus and other tmf classes. Section 2 reviews the sheaves of chiral differential operators (CDOs) over a complex manifold,…

Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of…

In this work, we introduce the notion of local and $2$-local $\delta$-derivations and describe local and $2$-local $\frac{1}{2}$-derivation of finite-dimensional solvable Lie algebras with filiform, Heisenberg, and abelian nilradicals.…