Simple Lie algebras which generalize Witt algebras

1997/12/30 by Ki-Bong Nam, Nam, Ki-Bong
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/9712293

openalex publication_date 1997/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new class of simple Lie algebras W(n,m) that generalize the Witt algebra by using "exponential" functions, and also a subalgebra W^*(n,m) thereof; and we show each derivation of W^*(1,0) can be written as a sum of an inner derivation and a scalar derivation. The Lie algebra W(n,m) is Z-graded and is infinite growth.

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• Supports of weight modules over Witt algebras
• Derivation-Simple Algebras and the Structures of Generalized Lie Algebras of Witt Type
• Quasi-derivations of Witt and related algebras
• On the restricted Lie algebra structure for the Witt Lie algebra in finite characteristic