In celebration of E. B. Dynkin's 70th birthday, this book presents current papers by those who participated in Dynkin's seminar on Lie groups and Lie algebras in the late 1950s and early 1960s. Dynkin had a major influence not only on mathematics, but also on the students who attended his seminar - many of whom are today's leading mathematicians in Russia and in the U.S. Dynkin's contributions to the theory of Lie groups is well known, and the survey paper by Karpelevich, Onishchik, and Vinberg allows readers to gain a deeper understanding of this work. Features several aspects of modern developments in Lie groups and Lie algebras, including...theory of invariants superalgebras arithmetic applications connections with mathematical physics. Providing insight on the extraordinary mathematical traditions that grew out of this important seminar, ""Lie Groups and Lie Algebras"" is a fitting celebration of Dynkin's achievements.
On the work of E. B. Dynkin in the theory of Lie groups by F. I. Karpelevich, A. L. Onishchik, and E. B. Vinberg Matrix Vieta theorem by D. Fuchs and A. Schwarz Integral geometry on real quadrics by S. Gindikin Dynkin diagrams in singularity theory by S. M. Gusein-Zade Variations on the triangular theme by A. A. Kirillov Vector fields and deformations of isotropic super-Grassmannians of maximal type by A. L. Onishchik and A. A. Serov $A \infty$ algebras and the cohomology of moduli spaces by M. Penkava and A. Schwarz On Hamburger's theorem by I. Piatetski-Shapiro and R. Raghunathan An analogue of M. Artin's conjecture on invariants for nonassociative algebras by V. L. Popov On reductive algebraic semigroups by E. B. Vinberg Crystal bases and the problem of reduction in classical and quantum modules by D. P. Zhelobenko.