Related papers: On Hadwiger-Alesker finiteness theorem
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…
In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.
This text provides an introduction and complements to some basic constructions and results in 2-representation theory of Kac-Moody algebras.
In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is…
We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem,…
$F-$Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). When $F>2$ not many finite-dimensional examples are known. In this paper we construct finite-dimensional $F-$Lie algebras $F>2$ by an inductive…
The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence…
We develop the theory of p-Lie algebras of finite Morley rank. In particular, we obtain a quite complete characterization in the soluble case
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
We prove a generalization of Gowers' theorem for $\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\mathrm{FIN}_{k}\rightarrow \mathrm{FIN}_{k-1}$, one considers all maps from $\mathrm{FIN}_{k}$ to $\mathrm{FIN}_{j}$ for…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.
We prove that the Fibonacci Lie algebra and the related just infinite self-similar Lie algebra are not finitely presented.
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…