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A class of non‐graded left‐symmetric algebraic structures on the Witt algebra
Author(s) -
Tang Xiaomin,
Bai Chengming
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000140
Subject(s) - mathematics , novikov self consistency principle , witt algebra , algebra over a field , pure mathematics , class (philosophy) , witt vector , algebraic number , non associative algebra , algebraic structure , quadratic algebra , universal enveloping algebra , algebra representation , cellular algebra , mathematical analysis , computer science , artificial intelligence
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.