A5052762947- Advanced Algebra and Geometry
- Algebraic Geometry and Number Theory
- Advanced Topics in Algebra
- Advanced Differential Equations and Dynamical Systems
- Finite Group Theory Research
- Homotopy and Cohomology in Algebraic Topology
- Algebraic structures and combinatorial models
- Geometric and Algebraic Topology
- Polynomial and algebraic computation
- Mathematics and Applications
- Rings, Modules, and Algebras
- Mathematical Dynamics and Fractals
- Advanced Combinatorial Mathematics
- Geometry and complex manifolds
- Commutative Algebra and Its Applications
- Meromorphic and Entire Functions
- Advanced Topology and Set Theory
- Advanced Numerical Analysis Techniques
- Advanced Algebra and Logic
- Analytic Number Theory Research
- semigroups and automata theory
- Advanced NMR Techniques and Applications
- Molecular spectroscopy and chirality
- graph theory and CDMA systems
- Holomorphic and Operator Theory
National Research University Higher School of Economics
2013-2024
Russian Academy of Sciences
2015-2024
Steklov Mathematical Institute
2015-2024
Imperial Valley College
2023
Institute of Applied Physics
2015
Bauman Moscow State Technical University
1997-2011
Vrije Universiteit Amsterdam
2011
University of Amsterdam
2011
Western University
2005
Royal Military College of Canada
2004
Here are reproduced slightly edited notes of my lectures on the classification discrete groups generated by complex reflections Hermitian affine spaces delivered in October 1980 at University Utrecht.
We give a classification of irreducible affine algebraic varieties which are quasihomogeneous with respect to regular action by connected linear group automorphisms and such that the isotropy subgroup point in general position contains maximal unipotent transformations. find criteria for normality factoriality varieties. compute divisor class complete description orbits
We construct models of finite-dimensional linear and projective irreducible representations a connected semisimple group G in systems on the variety G. establish an algebro-geometric criterion for linearizability representation explain meaning numerical characteristic arbitrary rational character maximal torus Using these results we compute Picard homogeneous space any algebraic H, prove homogeneity one-dimensional vector bundle over such relative to some covering Chern class bundle.
It is shown that each algebraic action of a simply connected reductive group on an affine variety can be contracted (in flat one-dimensional family actions) to canonical certain having some very special properties. and have many algebro-geometric properties in common. As application, we prove the Procesi-Kraft conjecture effect singularities closures orbits case spherical stabilizer are rational. assumed ground field has characteristic zero. Bibliography: 37 titles.
We prove that the variety of flexes algebraic curves degree $3$ in projective plane is an ideal theoretic complete intersection product a two-dimensional and nine-dimensional spaces.
We prove the following fact: if a connected algebraic group having no rational characters acts regularly on normal irreducible variety with periodic divisor class , then for orbit of point in general position to be closed, it is sufficient that an affine variety; moreover, affine, this condition also sufficient.
We classify up to G-isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group G = SL(2) which are defined over an algebraically closed field characteristic zero.
In this work it is proved that, for the regular action of a semisimple irreducible algebraic group G on an affine space, existence closed orbit maximum dimension equivalent to invariant open set at any point which stationary subgroup reductive. This result established manifolds special type (the so-called factorial manifolds). There are given several other conditions arbitrary manifold.
The classical Cayley map, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X right-arrow from bar left-parenthesis upper I Subscript n Baseline minus right-parenthesis plus Superscript negative 1"> <mml:semantics> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo stretchy="false">↦<!-- ↦ --></mml:mo> stretchy="false">(</mml:mo> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>−<!-- − stretchy="false">)</mml:mo>...
In this paper we find an explicit upper bound on the number of elements a minimal homogeneous system generators algebra invariants arbitrary connected semisimple linear group over algebraically closed field characteristic zero. We also show that approach to solution problem proposed by Dieudonné and Carrell contains error does not in fact achieve its aim.
Abstract Let k be a field of characteristic zero, let G connected reductive algebraic group over and 𝔤 its Lie algebra. ( ), respectively, (𝔤), the -rational functions on , 𝔤. The conjugation action itself induces adjoint We investigate question whether or not extensions )/ ) (𝔤)/ (𝔤) are purely transcendental. show that answer is same for reduce problem to case where simple. For simple groups we positive if split type A n C negative other types, except possibly 2 . key ingredient in proof...