Related papers: On simple groups definable in some valued fields

We study the domination monoid in various classes of structures arising from the model theory of henselian valuations, including RV-expansions of henselian valued fields of residue characteristic 0 (and, more generally, of benign valued…

We give a classification and complete algebraic description of groups allowing only finitely many (left multiplication invariant) circular orders. In particular, they are all solvable groups with a specific semi-direct product…

In this paper we describe all gradings by abelian groups without elements of order p, where p > 2 is the characteristic of the base field, on the simple graded Cartan type Lie algebras.

We prove that NIP valued fields of positive characteristic are henselian. Furthermore, we partially generalize the known results on dp-minimal fields to dp-finite fields. We prove a dichotomy: if K is a sufficiently saturated dp-finite…

We investigate what henselian valuations on ordered fields are definable in the language of ordered rings. This leads towards a systematic study of the class of ordered fields which are dense in their real closure. Some results have…

We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…

We continue the study of a class of topological $\mathcal{L}$-fields endowed with a generic derivation $\delta$, focussing on describing definable groups. We show that one can associate to an $\mathcal{L}_{\delta}$ definable group a type…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested…

In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.

We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…

In this paper we study elimination of imaginaries in some classes of henselian valued fields of equicharacteristic zero and residue field algebraically closed. The results are sensitive to the complexity of the value group. We focus first…

We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a…

Let $R$ be a finite-dimensional algebra over an algebraically closed field $F$ graded by an arbitrary group $G$. We prove that $R$ is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite…

Let A,B be finite dimensional G-graded algebras over an algebraically closed field K with char(K)=0, where G is an abelian group, and let Id_G(A) be the set of graded identities of A (res. Id_G(B)). We show that if A,B are G-simple then…

We develop a framework of motivic integration in the style of Hrushovski--Kazhdan in arbitrary Hensel minimal fields of equicharacteristic zero. Hence our work generalizes that of Hrushovski--Kazhdan and Yin, but applies more broadly to…

We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. These representations proved to be useful for the construction of abelian varieties…

It is shown that the classification theorems for semisimple algebraic groups in characteristic zero can be derived quite simply and naturally from the corresponding theorems for Lie algebras by using a little of the theory of tensor…