On Ado theorem(s)

Venue:  Seminar Room “-1” – Department of Mathematics
Time: 14:30

• Speaker: Pasha Zusmanovich (University of Ostrava)

Abstract:
The Ado theorem is a basic fact in the theory of Lie algebras saying that any finite-dimensional Lie algebra admits a faithful finite-dimensional representation. Somewhat surprisingly, the standard proof of such a basic fact utilizes non-trivial facts about universal enveloping algebras and is quite involved. I will present an entirely different proof intrinsic to the category of finite-dimensional Lie algebras, but valid for nilpotent algebras only.
If time will permit, I will also discuss the failure of a variant of this theorem for "commutative analogs" of Lie algebras, i.e. commutative algebras satisfying the Jacobi identity.

Contact people: Andrea Caranti - Willem de Graaf