Related papers: Notes on Central Extensions
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
This is a review article based on a mini-course comprised of four talks given by the author at Berkeley.
In arXiv:2206.00549, transference results between multilinear Fourier and Schur multipliers on noncommutative $L_p$-spaces were shown for unimodular groups. We propose a suitable extension of the definition of multilinear Fourier…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
This article is an exposition of the 1967 Annals paper by Parthasarathy, Ranga Rao, and Varadarajan, on irreducible admissible Harish-Chandra modules over complex semisimple Lie groups and Lie algebras. It was written in Winter 2012 to be…
This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…
In this paper, we describe restricted one-dimensional central extensions of all finite dimensional simple restricted Lie algebras defined over fields of characteristic $p\ge 5$.
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors…
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey…
We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…
These notes are based on the course given at the School of Geometry, University Kasdi Merbah (Ouargla) 2012. The aim of the course was the deformation quantization of Poisson Lie groups. In these notes we only review Kontsevich's formality…
In this paper we study the notion of isoclinism on Lie-central extensions of Leibniz algebras, this yields to introduce the concept of Lie-isoclinic Leibniz algebras. We provide several equivalent conditions under which Leibniz algebras are…
We present the method for finding of the nonlinear Poisson-Lie groups structures on the vector spaces and for their quantization. For arbitrary central extension of Lie algebra explicit formulas of quantization are proposed.
These lecture notes provide a pedagogical introduction, with exercises, to the techniques used in attempts to construct vacua with stabilised moduli in string theory. The reader is only assumed to have a basic knowledge of general…
Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their…
Lecture notes for the proceedings of the workshop "Algebraic Combinatorics related to Young diagram and statistical physics", Aug. 6-10 2012, I.I.A.S., Nara, Japan.
These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…