相关论文: An introduction to Heisenberg groups

We introduce a general class of Heisenberg groups motivated by applications of algebraic Fourier theory. Basic properties are examined from a homological perspective.

An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.

Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.

We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.

This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.

This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.

We present an accessible introduction to basic results on groups of intermediate growth.

This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.

Expanded lecture notes. Preliminary version, comments are welcome.

The notes provide a short introduction to de Branges--Rovnyak spaces. They cover some basic facts and are intended to give the reader a taste of the theory, providing sufficient motivation to make it interesting.

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…

These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.

These informal notes deal with p-adic versions of Heisenberg groups and related matters.

In this note we describe the embeddings of the Heisenberg group into the Cremona group.

This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience. The objective of this paper is to help the reader feel…

We provide a partial solution to the isoperimetric problem in the Heisenberg group.

This paper describes in basic terms what a "Thin Group" is, as well as its uses in various subjects.

This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…

This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.

These informal notes concern some basic themes of harmonic analysis related to representations of groups.