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 These papers will not be published elsewhere.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.
Preface by A. L. Onishchik, V. L. Popov, and E. B. Vinberg $G$-manifolds with one-dimensional orbit space by A. V. Alekseevskii and D. V. Alekseevskii Arithmetic crystallographic groups generated by reflections and reflective hyperbolic lattices by V. O. Bugaenko Invariant algebras by A. G. Elashvili On the existence of Galois sections by L. Yu. Galitskii On some cohomology invariants of compact homogeneous manifolds by V. V. Gorbatsevich Explicit form of certain multivector invariants by A. A. Katanova On the birational geometry of the space of ternary quartics by P. I. Katsylo Rationality of the module variety of mathematical instantons with $c 2=5$ by P. I. Katsylo Holomorphic vector fields on super-Grassmannians by A. L. Onishchik and A. A. Serov Affine quasihomogeneous normal $SL 2$-varieties: Hilbert function and blow-ups by D. I. Panyushev Complexity of quasiaffine homogeneous varieties, $t$-decompositions, and affine homogeneous spaces of complexity $1$ by D. I. Panyushev On the "Lemma of Seshadri" by V. L. Popov Coregular algebraic linear groups locally isomorphic to $SL 2$ by D. A. Shmelkin An example of a nonarithmetic discrete group in the complex ball by O. V. Shvartsman Free subsemigroups of the affine group, and the Schoenflies-Bieberbach theorem by G. A. Soifer.