Lie Theory

7. Gave in 1947 a short proof of the Baker-Campbell-Hausdorff formula
8. Showed that nilpotent elements in semisimple algebras can be extended to sl(2) triples
12. Used the exceptional algebra G_2 in atomic spectroscopy
13. Classified real forms of semisimple Lie algebras
15. Introduced in 1935 an important operator in representation theory
16. Revitalized in 1962 the theory of Lie groups in differential equations
18. Pioneer in the study of Lie algebras in characteristic p>0
21. Gives name to a "magic square"
22. Gives name to a decomposition theorem into semisimple and solvable parts

1. Developed a fundamental technique in representation theory
2. Gave a first classification of complex simple Lie algebras
3. Gave with Zippin a solution to the Hilbert 5th problem
4. Coined the term "Lie algebra"
5. Analyzed with Nijenhuis the notion of rigidity
6. Gave in 1891 a first classification of nilpotent algebras of low order
9. Developed the structure theory of solvable real Lie algebras
10. Analyzed the uniqueness of semisimple components in the Wedderburn decomposition
11. Studied Lie algebras of vector fields in connection with superposition formulae
14. Showed the existence of nonlinear Lie groups
17. Gives with Gel'fand the name to a class of patterns
19. Gives name to a criterion on nilpotent Lie algebras
20. Author of the first monograph on Lie groups published in the USSR