Lie algebras, algebraic groups, Hopf algebras, Galois theory
As a junior undergraduate at Antioch College in 1959-60, I studied permutation group theory, differential geometry, and functional analysis from Helmut Wielandt at the University of Tuebingen, Germany. Upon graduation, I entered graduate school at Yale University in 1961, receiving my PhD in 1965 under the supervision of George Seligman. From 1965 to 1967, I was an instructor at Yale University. In 1967-68 I studied with Jacques Tits at the University of Bonn as National Science Foundation Postdoctoral Fellow. After a summer as one of three NSF lecturers at the Bowdoin College Advanced Algebraic Groups NSF Summer Science Institute, I joined the faculty at the University of Michigan in the fall of 1968. In 1972-73, I was visiting professor at the California Institute of Technology. In 1982-83, I taught algebraic group theory and did research on Lie algebras at the University of Chicago.
I have some 50 publications including 5 books (two co-authored with I.N. Herstein), including Abstract Lie Algebras (M.I.T. Press, 1972), Structure of Fields (Springer Verlag, 1974), and Matrix Theory and Linear Algebra (Macmillan, 1988). I was the editor for Lie Algebras and Related Topics (Springer Verlag Lecture Notes in Mathematics 933, 1981).
My current research is concerned with (primarily simple infinite dimensional) Lie algebras, Hopf algebras, associative algebras, and associated algebraic structures. It is also concerned with Galois theory of commutative rings.