Related papers: Chevalley's theorem for affine Nash groups

We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a…

The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank at least 2 over a class of commutative rings that includes the localizations of 1-generated…

We prove an explicit inverse Chevalley formula in the equivariant $K$-theory of semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley formula, we mean a formula for the product of an equivariant scalar with a Schubert…

We give an explicit combinatorial Chevalley-type formula for the equivariant K-theory of generalized flag varieties G/P which is a direct generalization of the classical Chevalley formula. Our formula implies a simple combinatorial model…

By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic…

This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we…

A group G is sharply 2-transitive if it admits a faithful permutation representation that is transitive and free on pairs of distinct points. Conjecturally, for all such groups there exists a near-field N (i.e. a skew field that is…

We present a new algorithm deciding if the intersection of a quasiconvex subgroup of a negatively curved group with a conjugate is finite. We also give a short proof of decidability of the membership problem for quasiconvex subgroups of…

Let $k$ be a perfect field. Assume that the characteristic of $k$ satisfies certain tameness assumptions \eqref{tameness}. Let $\mathcal O_{_n} := k\llbracket z_{_1}, \ldots, z_{_n}\rrbracket$ and set $K_{_n} := \text{Fract}~\cO_{_n}$. Let…

A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming…

Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…

In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed…

Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…

We revisit localisation and patching method in the setting of Chevalley groups. Introducing certain subgroups of relative elementary Chevalley groups, we develop relative versions of the conjugation calculus and the commutator calculus in…

We provide a new and much simpler structure for quasi-ideal adequate transversals of abundant semigroups in terms of spined products, which is similar in nature to that given by Saito for weakly multiplicative inverse transversals of…

For a finite group acting on a polynomial ring, the Chevalley-Shephard-Todd Theorem proves that the fixed subring is isomorphic to a polynomial ring if and only if the group is generated by pseudo-reflections. In recent years, progress was…

This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…

We prove that for any finitely generated relatively hyperbolic group G and any symmetric endomorphism f of G with relatively quasiconvex image, Fixf is relatively quasiconvex subgroup of G.

In this note the Chernoff Theorem is used to approximate evolution semigroups constructed by the procedure of subordination. The considered semigroups are subordinate to some original, unknown explicitly but already approximated by the same…

We lay the foundations for the study of relatively quasiconvex subgroups of relatively hyperbolic groups. These foundations require that we first work out a coherent theory of countable relatively hyperbolic groups (not necessarily finitely…