A lower central series for split Hopf algebras with involution

On split exact sequences Hopf algebras

A Poincaré-birkhoff-witt Theorem for Hopf Algebras with Central Hopf Algebra Coradical

We show that over algebraically closed fields of characteristic zero a Hopf algebra with central Hopf algebra coradical has a PBW basis after some localization of the coradical.

Homotopy Lie algebras, lower central series and the Koszul property

Let X and Y be finite-type CW–complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k–rescaling of the rational cohomology ring of X . Assume H∗(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra π∗(ΩY ) ⊗ Q equals, up to k–rescaling, the graded rational Lie algebra associated to the lower central series of π1(X). If Y is a formal space, this equali...

On the Lower Central Series of Pi-algebras

In this paper we study the lower central series {Li}i≥1 of algebras with polynomial identities. More specifically, we investigate the properties of the quotients Ni = Mi/Mi+1 of successive ideals generated by the elements Li. We give a complete description of the structure of these quotients for the free metabelian associative algebra A/(A[A,A][A,A]). With methods from Polynomial Identities the...

Homotopy Lie Algebras , Lower Central Series , and the Koszul