Related papers: Real structures on complex algebraic varieties wit…
We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general…
We survey some recent developments and applications of the study of the rigidity properties of natural algebraic actions of multidimensional abelian groups.
In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
In this paper we give a way of equipping the derivation algebra of a group algebra with the structure of a graded algebra. The derived group is used as the grading group. For the proof, the identification of the derivation with the…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.
We provide a complete description of normal affine algebraic varieties over the real numbers endowed with an effective action of the real circle, that is, the real form of the complex multiplicative group whose real locus consists of the…
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real…
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…
In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…
We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent developments on the genus problem for simple algebraic…
We introduce the notion of a subregular subalgebra, which we believe is useful for classification of subalgebras of Lie algebras. We use it to construct a non-regular invariant generalized complex structure on a Lie group. As an…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the…
We survey new results on finite groups of birational transformations of algebraic varieties.
This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…
We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of three-dimensional vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked…