Advances in Soviet Mathematics 1992; 204 pp; hardcover Volume: 8 ISBN10: 0821841076 ISBN13: 9780821841075 List Price: US$145 Member Price: US$116 Order Code: ADVSOV/8
 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 codirector, 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 KacMoody groups and algebras. This collection of papers presents a snapshot of the research activities of this wellestablished 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 These papers will not be published elsewhere.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 onedimensional 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 superGrassmannians
 D. I. Panyushev  Affine quasihomogeneous normal \(SL_2\)varieties: Hilbert function and blowups
 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 SchoenfliesBieberbach theorem
