For the past thirty years, E. B. Vinberg and L. A. Onishchik have conducted a seminar on Lie groups at Moscow University; about five years ago V. L. Popov became the third co-director, and the range of topics expanded to include invariant theory. Today, the seminar encompasses such areas as algebraic groups, geometry and topology of homogeneous spaces, and Kac-Moody groups and algebras. This collection of papers presents a snapshot of the research activities of this well-established seminar, including new results in Lie groups, crystallographic groups, and algebraic transformation groups. These papers will not be published elsewhere. Readers will find this volume useful for the new results it contains as well as for the open problems it poses.

Readership

Graduate students and researchers in pure mathematics.

Table of Contents

• A. L. Onishchik, V. L. Popov, and E. B. Vinberg -- Preface
• A. V. Alekseevskiĭ and D. V. Alekseevskiĭ -- \(G\)-manifolds with one-dimensional orbit space
• V. O. Bugaenko -- Arithmetic crystallographic groups generated by reflections and reflective hyperbolic lattices
• A. G. Elashvili -- Invariant algebras
• L. Yu. Galitskiĭ -- On the existence of Galois sections
• V. V. Gorbatsevich -- On some cohomology invariants of compact homogeneous manifolds
• A. A. Katanova -- Explicit form of certain multivector invariants
• P. I. Katsylo -- On the birational geometry of the space of ternary quartics
• P. I. Katsylo -- Rationality of the module variety of mathematical instantons with \(c_2=5\)
• A. L. Onishchik and A. A. Serov -- Holomorphic vector fields on super-Grassmannians
• D. I. Panyushev -- Affine quasihomogeneous normal \(SL_2\)-varieties: Hilbert function and blow-ups
• D. I. Panyushev -- Complexity of quasiaffine homogeneous varieties, \(t\)-decompositions, and affine homogeneous spaces of complexity \(1\)
• V. L. Popov -- On the "Lemma of Seshadri"
• D. A. Shmel'kin -- Coregular algebraic linear groups locally isomorphic to \(SL_2\)
• O. V. Shvartsman -- An example of a nonarithmetic discrete group in the complex ball
• G. A. Soĭfer -- Free subsemigroups of the affine group, and the Schoenflies-Bieberbach theorem