Related papers: Introduction to Vertex Algebras
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
Foundations of the theory of vertex algebras are extended to the non-Archimedean setting.
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
In this paper we build an abstract description of vertex algebras from their basic axioms. Starting with Borcherds' notion of a vertex group, we naturally construct a family of multilinear singular maps parameterised by trees. These…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
Expanded lecture notes. Preliminary version, comments are welcome.
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
Logarithmic vertex algebras were introduced in our previous paper, motivated by logarithmic conformal field theory. Non-local Poisson vertex algebras were introduced by De Sole and Kac, motivated by the theory of integrable systems. We…
Since Leibniz algebras were introduced by Loday as a generalization of Lie algebras, there has been a lot of interest in which results of the latter extend to the former. Cyclic algebras, those generated by one element, are a useful tool…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are {\em simple currents} associated with semisimple weight one primary vectors. In the case that the…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
The goal of this paper is to make the vertex operator algebra approach to mirror symmetry accessible to algebraic geometers. Compared to better-known approaches using moduli spaces of stable maps and special Lagrangian fibrations, this…
An overview of the authors' ideas about the process of completing a $p$-adically normed space in the setting of vertex operator algebras. We focus in particular on the $p$-adic Heisenberg VOA and its connections with $p$-adic modular forms.
This text provides an introduction and complements to some basic constructions and results in 2-representation theory of Kac-Moody algebras.