Almost Inner Derivations of Affinizations of Minimal Q-graded Subalgebras

2025/07/13 by Shen, Yaxin, Xiandong Wang, Wang, Xiandong
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.09484

openalex publication_date 2025/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Minimal Q-graded subalgebras of semisimple Lie algebras are introduced, and it is proved that their derived algebras are abelian. Almost inner derivations of minimal Q-graded subalgebras are investigated, they are all inner derivations. Based on these Lie algebras, a decomposition formula is obtained for derivations of loop algebras, and almost inner derivations of affinizations are determined.

Citations

• Almost inner derivations of 2-step nilpotent Lie algebras of genus 2
• Almost inner derivations of Lie algebras II
• Almost inner derivations of Lie algebras
• Derivations of tensor product of algebras

Related

• Derivations of Twisted Loop Algebras of Minimal Q-graded Subalgebras
• Almost inner derivations of Lie superalgebras
• Almost inner derivations of Lie algebras
• Almost inner derivations of Lie algebras II
• A computational approach to almost-inner derivations