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- W3138307302 abstract "This chapter gives a brief introduction to pre-Lie algebras, with emphasis on their connections with some related structures. Pre-Lie algebras have several other names: left-symmetric algebra, right-symmetric algebra, pre-Lie algebra, Quasi-associative algebra, and Vinberg algebra or Koszul algebra or Koszul–Vinberg algebra. Some subclasses of pre-Lie algebras are very interesting. Some of them were even introduced and then developed independently. The chapter introduces some background information and different motivations of introducing the notion of pre-Lie algebra. It also introduces some basic properties of pre-Lie algebras including some comments on the studies of structure theory and representation theory and some classification results. The chapter gives the constructions of pre-Lie algebras from some known structures such as commutative associative algebras, Lie algebras, associative algebras and linear functions. It focuses on the close relationship between pre-Lie algebras and the classical Yang–Baxter equation." @default.
- W3138307302 created "2021-03-29" @default.
- W3138307302 creator A5014897749 @default.
- W3138307302 date "2021-03-19" @default.
- W3138307302 modified "2023-10-17" @default.
- W3138307302 title "An Introduction to Pre‐Lie Algebras" @default.
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- W3138307302 doi "https://doi.org/10.1002/9781119818175.ch7" @default.
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