Extensions of Enveloping Algebras Via Anti-cocommutative Elements

Abstract

We know that given a connected Hopf algebra H, the universal enveloping algebra U(P(H)) embeds in H as a Hopf subalgebra. Depending on P(H), we show that there may be another enveloping algebra (not as a Hopf subalgebra) within H by using anti-cocommutative elements. Thus, this is an extension of enveloping algebras with regards to the Hopf structure. We also use these discoveries to apply to global dimension, and finish with antipode behavior and future research projects.