Date of Award
Doctor of Philosophy
Allen D. Bell
Allen D. Bell, Craig R. Guilbault, Ian M. Musson, Jeb F. Willenbring, Yi M. Zou
Anti-cocommutative, Connected Algebra, Enveloping Algebra, Global Dimension, HOPF Algebra, Non-commutative Algebra
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.
Yee, Daniel Owen, "Extensions of Enveloping Algebras Via Anti-cocommutative Elements" (2017). Theses and Dissertations. 1728.