Related papers: Abstract simplicity of complete Kac-Moody groups o…

Let G be a complete Kac-Moody group of rank n \geq 2 over the finite field of order q, with Weyl group W and building \Delta. We first show that if W is right-angled, then for all q \neq 1 mod 4 the group G admits a cocompact lattice \Gamma…

Kac-Moody symmetric spaces have been introduced by Freyn, Hartnick, Horn and the first-named author for centered Kac-Moody groups, that is, Kac-Moody groups that are generated by their root subgroups. In the case of non-invertible…

This survey paper presents the discrete group viewpoint on Kac-Moody groups. Over finite fields, the latter groups are finitely generated; they act on new buildings enjoying remarkable negative curvature properties. The study of these…

Let $G$ be a simply connected Lie group with Lie algebra $\mathfrak{g}$ and denote by $\mathrm{C}_{\bullet}(G)$ the DG Hopf algebra of smooth singular chains on $G$. In a companion paper it was shown that the category of sufficiently smooth…

Let $A$ be an elementary abelian $r$-group with rank at least $3$ that acts faithfully on the finite $r'$-group $G$. Assume that $G$ is $A$-simple, so that $G = K_{1} \times\cdots\times K_{n}$ where $K_{1},\ldots,K_{n}$ is a collection of…

In this paper we give an elementary proof of certain finiteness results about affine Kac-Moody groups over a local non-archimedian field K. Our results imply those proven earlier by Braverman-Kazhdan, Braverman-Finkelberg-Kazhdan and…

A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold $\mathcal{M}$ to a finite-dimensional Lie group, by means of complete orthonormal bases for a Hermitian inner product on the manifold and a…

Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite…

We study the topology of spaces related to Kac-Moody groups. Given a split Kac-Moody group over the complex numbers, let K denote the unitary form with maximal torus T having normalizer N(T). In this article we study the cohomology of the…

In a previous paper we define a Curtis-Tits group as a certain generalization of a Kac-Moody group. We distinguish between orientable and non-orientable Curtis-Tits groups and identify all orientable Curtis-Tits groups as Kac-Moody groups…

In this study, we try to generalize Bruhat-Tits's theory to the case of a Kac-Moody group, that is to define an affine building for a Kac-Moody group over a local field. Actually, we will obtain a geometric space wich lacks some of the…

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$.…

We construct holomorphic loop groups and their associated affine Kac-Moody groups and prove that they are tame Fr\'echet manifolds. These results form the functional analytic basis for the theory of affine Kac-Moody symmetric spaces,…

We construct a map from the classifying space of a discrete Kac-Moody group over the algebraic closure of the field with p elements to the classifying space of a complex topological Kac-Moody group and prove that it is a homology…

In \cite{CM06} Caprace and M\"uhlherr solved the isomorphism problem for Kac-Moody groups of non-spherical type over finite fields of cardinality at least $4$. In this paper we solve the isomorphism problem for RGD-systems (e.g.\ Kac-Moody…

Let $A$ be a symmetrisable generalised Cartan matrix, and let $\mathfrak g(A)$ be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question on the structure of $\mathfrak g(A)$: given two homogeneous…

Let G be a split Kac-Moody group over a non-archimedean local field. We define a completion of the Iwahori-Hecke algebra of G. We determine its center and prove that it is isomorphic to the spherical Hecke algebra of G using the Satake…

The group of simplicial automorphisms of a Tits-Kac-Moody ininite building of thickness q associated to a cocompact reflexion group with fundamental domain a simplex, is Kazhdan for q sufficiently large. Thus we obtain families of new…

For a split Kac-Moody group (in J. Tits' definition) over a field endowed with a real valuation, we build an ordered affine hovel on which the group acts. This construction generalizes the one already done by S. Gaussent and the author when…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…