**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

1995; 202 pp; Hardcover

MSC: Primary 22; 57; Secondary 14; 15; 17; 42; 44; 53; 58

Print ISBN: 978-0-8218-0454-4

Product Code: TRANS2/169

Print ISBN: 978-0-8218-0454-4

Product Code: TRANS2/169

List Price: $114.00

Individual Member Price: $91.20

**Electronic ISBN: 978-1-4704-3380-2
Product Code: TRANS2/169.E**

List Price: $114.00

Individual Member Price: $91.20

# Lie Groups and Lie Algebras: E. B. Dynkin’s Seminar

Share this page *Edited by *
*S. G. Gindikin; E. B. Vinberg*

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

## Lie Groups and Lie Algebras: E. B. Dynkin's Seminar

- Cover Cover11
- Frontispiece iv5
- Title page v6
- Copyright page vi7
- Contents vii8
- Preface ix10
- On the work of E. B. Dynkin in the theory of Lie groups 114
- Matrix Vieta theorem 1528
- Integral geometry on real quadrics 2336
- Dynkin diagrams in singularity theory 3346
- Variations on the triangular theme 4356
- Vector fields and deformations of isotropic super-Grassmannians of maximal type 7588
- 𝐴_{∞} algebras and the cohomology of moduli spaces 91104
- On Hamburger’s theorem 109122
- An analogue of M. Artin’s conjecture on invariants for nonassociative algebras 121134
- On reductive algebraic semigroups 145158
- Crystal bases and the problem of reduction in classical and quantum modules 183196
- Back Cover Back Cover1217