Related papers: String C-group representations of almost simple gr…
The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
This work provides a classification of string C-groups of order 2m and exponent at least 2^(m - 3). Prior to the classification, we complete the list of groups of exponent 2^(m - 3) and rank at least 3. The main result states that, aside…
We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split groups done by Kac to the non-split quasi-split case. For the…
We give an overview of some recent developments in semigroup C*-algebras.
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.
We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.
The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…
A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…
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…
We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from…
Language is a social phenomenon and variation is inherent to its social nature. Recently, there has been a surge of interest within the computational linguistics (CL) community in the social dimension of language. In this article we present…
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
Suzuki recently gave constructions of non-discrete examples of locally compact C*-simple groups and Raum showed C*-simplicity of the relative profinite completions of the Baumslag-Solitar groups by using Suzuki's results. We extend this…
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
The reduced C*-algebra of a countable linear group G is shown to be simple if and only if G has no nontrivial normal amenable subgroups. Moreover, these conditions are shown to be equivalent to the uniqueness of tracial state on the…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes.
The use of compositions simplifies some aspects of the theory of numerical semigroups. We illustrate this by giving a new proof for the asymptotic number C((1 + $\sqrt$ 5)/2) g of numerical semigroups of genus g and by describing the…