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.

Readership

Researchers, graduate students, and physicists interested in Lie groups, Lie algebras, and related areas.

Table of Contents

• F. I. Karpelevich, A. L. Onishchik, and E. B. Vinberg -- On the work of E. B. Dynkin in the theory of Lie groups
• D. Fuchs and A. Schwarz -- Matrix Vieta theorem
• S. Gindikin -- Integral geometry on real quadrics
• S. M. Gusein-Zade -- Dynkin diagrams in singularity theory
• A. A. Kirillov -- Variations on the triangular theme
• A. L. Onishchik and A. A. Serov -- Vector fields and deformations of isotropic super-Grassmannians of maximal type
• M. Penkava and A. Schwarz -- $A_\infty$ algebras and the cohomology of moduli spaces
• I. Piatetski-Shapiro and R. Raghunathan -- On Hamburger's theorem
• V. L. Popov -- An analogue of M. Artin's conjecture on invariants for nonassociative algebras
• E. B. Vinberg -- On reductive algebraic semigroups
• D. P. Zhelobenko -- Crystal bases and the problem of reduction in classical and quantum modules