Related papers: The tame Butcher group

We introduce an extension of the (tame) polynomial automorphism group over finite fields: the profinite (tame) polynomial automorphism group, which is obtained by putting a natural topology on the automorphism group. We show that most known…

The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…

We introduce a combinatorial property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. We also define…

We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular…

We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: (a) groups of germs…

Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant…

Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two…

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…

We consider a specific class of infinite dimensional $p$-adic Lie groups, i.e., a sort of diffeomorphism groups on $p$-adic ball $\operatorname{Diff}^{\operatorname{an}}(B_\epsilon)$. It turns out that this group has a natural logarithmic…

We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of these. For toral…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

We give a classification theorem of certain geometric objects, called torsors over the sheaf of K-theory spaces, in terms of Tate vector bundles. This allows us to present a very natural and simple, alternative approach to the Tate central…

We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application,…

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups…

We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…

A Lie system is a non-autonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, a so-called (nonlinear) superposition rule of a finite number of particular solutions…

Let M be a topological manifold modelled on topological vector spaces, which is the union of an ascending sequence of such manifolds M_n. We formulate a mild condition ensuring that the k-th homotopy group of M is the direct limit of the…

In this paper we continue the study of group representations which are counterexamples to the Ize conjecture. As in the previous papers by Lauterbach [14] and Lauterbach & Matthews [15] we find new infinite series of finite groups leading…

A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of…