# Dan Petersen: Lie, associative and commutative quasi-isomorphism

**Time: **
Wed 2019-03-27 13.15 - 14.15

**Lecturer: **
Dan Petersen (SU)

**Location: ** Room 3418, KTH

Abstract: We prove that rationally, two commutative dg algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. We also prove a Koszul dual theorem, that two dg Lie algebras are quasi-isomorphic if and only if their universal enveloping algebras are quasi-isomorphic. The latter result is new already for classical (non-dg) algebras, in which case it says that two Lie algebras over a field of characteristic zero are isomorphic if and only if their universal enveloping algebras are isomorphic as associative algebras. This builds on and generalizes work of Saleh.