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.
