Extending Enveloping Algebras via Anti-Cocommutative Elements

2017/05/29 by Daniel Yee, Yee, Daniel
Mathematics · #16T05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1705.10228

openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Anti-cocommutativity was introduced by Wang, Zhuang, Zhang (2013) in their paper Coassociative Lie algebras. Since universal enveloping algebras of Lie algebras are connected Hopf algebras, we extend enveloping algebras using the notion of anti-cocommutative elements. This concept is the main focus of this thesis. We separate the results (Chapter 4) into four parts: 1) Lie algebras containing anti-cocommutative elements; 2) Extending enveloping algebras using anti-cocommutative elements; 3) A global dimension problem for connected Hopf algebras; 4) Properties of the antipode of some connected Hopf algebras.

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