Extensions of Enveloping Algebras by Anti-Cocommutative Elements

2017/11/10 by Daniel Yee, Yee, Daniel
Computer Science · Mathematics · #16T05 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1711.03708

openalex publication_date 2017/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Anti-cocommutative elements were introduced by Wang, Zhang, Zhuang (2013) in their paper Coassociative Lie Algebras. We use this notion to extend universal enveloping algebras of Lie algebras with regards to their Hopf structure, and see if these connected Hopf algebras are enveloping algebras. Furthermore, we apply these results to compare global dimension of connected Hopf algebras and the dimension of their corresponding Lie algebras of primitive elements. Title has been renamed to "GK-Dimension of some Connected Hopf Algebras".

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