Читать книгу Algebra and Applications 2 - Группа авторов - Страница 26

Pre-Lie algebras are sometimes called Vinberg algebras, as they appear in the work of Vinberg (1963) under the name “left-symmetric algebras” on the classification of homogeneous cones. They appear independently at the same time in the work of Gerstenhaber (1963) on Hochschild cohomology and deformations of algebras, under the name “pre-Lie algebras”, which is now the standard terminology. The term “chronological algebras” has also been used sometimes, for example, in the fundamental work of Agrachev and Gamkrelidze (1981). The notion itself can, however, be traced back to the work of Cayley (1857) which, in modern language, describes the pre-Lie algebra morphism Fa from the pre-Lie algebra of rooted trees into the pre-Lie algebra of vector fields on ℝⁿ, sending the one-vertex tree to a given vector field a. For a survey emphasizing geometric aspects, see Burde (2006).