Related papers: Linearization problem for finite subgroups of the …
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
In this paper we give a solution to Zariski's problem of analytic classification of plane branches.
We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any…
We classify all linearly compact simple Jordan superalgebras over an algebraically closed field of characteristic zero. As a corollary, we deduce the classification of all linearly compact unital simple generalized Poisson superalgebras.
We consider the problem of counting the number of rational points of bounded height in the zero-loci of Brauer group elements on semi-simple algebraic groups over number fields. We obtain asymptotic formulae for the counting problem for…
We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can…
The group classification problem for the class of (1+1)-dimensional linear $r$th order evolution equations is solved for arbitrary values of $r>2$. It is shown that a related maximally gauged class of homogeneous linear evolution equations…
We classify all finite groups of essential dimension 2 over an algebraically closed field of characteristic 0.
We compute the completion of the special linear group over the coordinate ring of a curve over a number field $k$ relative to its representation in $\slnk$, and relate this to the study of $K_2$ of the curve.
We obtain a solution to a bordism version of Gromov's linearity problem over a large family of acyclic groups, for manifolds with arbitrary dimension. Every group embeds into some acyclic group in this family. Thus, the linear bordism…
The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a…
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. We focus on solvable Lie algebras of small dimensions over fields of arbitrary characteristic. We prove, over an…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
We compute the completion of the groups SL_n(Z[t]) and SL_n(Z[t,t^{-1}]) relative to the obvious homomorphisms to SL_n(Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second…
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…
We summarize exact solutions of closed superstrings in a constant magnetic field, from a view point of the regularization criterion. Some models will be excluded according to this criterion. The spectrum-generating algebra is also…
We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.
We construct a log algebraic version of the homotopy sequence for a quasi-projective normal crossing log variety over a log point of characteristic zero and prove some exactness properties of it. Our proofs are purely algebraic.
A proof of freeness of the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic. A description of the abelianizations of the fundamental…