[BOOK][B] An introduction to Kac–Moody groups over fields

T Marquis - 2018 - ems.press
The interest for Kac–Moody algebras and groups has grown exponentially in the past
decades, both in the mathematical and physics communities. In physics, this interest has …

High-dimensional expanders from Kac–Moody–Steinberg groups

LG de Peralta, I Valentiner-Branth - European Journal of Combinatorics, 2025 - Elsevier
High-dimensional expanders are a generalization of the notion of expander graphs to
simplicial complexes and give rise to a variety of applications in computer science and other …

Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients

PE Caprace, M Kassabov - Transactions of the American Mathematical …, 2023 - ams.org
We construct new families of groups with property (T) and infinitely many alternating group
quotients. One of those consists of subgroups of $\mathrm {Aut}(\mathbf {F} _ {p}[x_1,\dots …

Hyperbolic generalized triangle groups, property (T) and finite simple quotients

PE Caprace, M Conder, M Kaluba… - Journal of the London …, 2022 - Wiley Online Library
We construct several series of explicit presentations of infinite hyperbolic groups enjoying
Kazhdan's property (T). Some of them are significantly shorter than the previously known …

SL2 representations and relative property (T)

Z Zhang - Journal of Algebra, 2024 - Elsevier
We investigate relative property (T) of Kazhdan-Margulis for (SL 2 (R)⋉ R n, R n), mainly
where R is a discrete finitely generated commutative ring. The action of SL 2 (R) on R n is …

High dimensional expanders and coset geometries

T Kaufman, I Oppenheim - arxiv preprint arxiv:1710.05304, 2017 - arxiv.org
High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only
known construction of bounded degree high dimensional expanders is based on …

Link conditions for cubulation

CJ Ashcroft - International Mathematics Research Notices, 2023 - academic.oup.com
We provide a condition on the links of polygonal complexes that is sufficient to ensure
groups acting properly discontinuously and cocompactly on such complexes contain a …

High dimensional expanders and coset geometries

T Kaufman, I Oppenheim - European Journal of Combinatorics, 2023 - Elsevier
High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only
known construction of bounded degree high dimensional expanders is based on …

[PDF][PDF] Unitary representations and Kazhdan's property (T)

A Loué, PE Caprace - 2021 - dial.uclouvain.be
Kazhdan's property (T) is a rigidity property of unitary representations of groups. More
precisely, we say that a group has property (T) if, whenever a unitary representation almost …

Groups over Fields

T Marquis - ems.press
The interest for Kac–Moody algebras and groups has grown exponentially in the past
decades, both in the mathematical and physics communities. In physics, this interest has …