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A class of non-graded left-symmetric algebraic structures on the Witt algebra

✍ Scribed by Xiaomin Tang; Chengming Bai

Publisher: John Wiley and Sons
Year: 2012
Tongue: English
Weight: 199 KB
Volume: 285
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.201000140

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✦ Synopsis

Abstract

We classify the compatible left‐symmetric algebraic structures on the Witt algebra satisfying certain non‐graded conditions. It is unexpected that they are Novikov algebras. Furthermore, as applications, we study the induced non‐graded modules of the Witt algebra and the induced Lie algebras by Novikov‐Poisson algebras’ approach and Balinskii‐Novikov's construction.

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