Dr. Elizabeth Gillaspy (Mathematics Department, Univ. of Montana)

3/6/2023  4:10pm

Abstract:  D. Luminet proved in 1987 that nilpotent Lie algebras are the only Lie algebras whose enveloping algebra embeds in a Banach algebra.  Together with Wend Werner, we have discovered that the enveloping algebra of a nilpotent Lie algebra can always be embedded inside a C*-algebra.  However, there are many choices about how to do so, and no evident candidate for a preferred or universal C*-algebra.  In this talk, I will discuss some of our favorite candidates for "the C*-algebra of a nilpotent Lie algebra" and the pros and cons of each.