Classification of Some Simple Graded Pre-lie Algebras of Growth One
نویسندگان
چکیده
The notion of pre-Lie algebra can be seen as a weakened form of associative algebra, still giving a Lie algebra by anti-symmetrization. It has been introduced by Gerstenhaber in his work on deformations of algebras [Ger64]. More recently, it has been studied from the point of view of operad theory and seen to be related to rooted trees [CL01]. The motivating problem for this paper is the classification of infinitedimensional simple graded pre-Lie algebras of finite growth over C. This seems to be a difficult problem, as it implies in particular the same classification for associative algebras. The analogous problem for Lie algebras has been solved by Mathieu in [Mat91, Mat92]. The first step in the case of Lie algebras was the classification for growth not greater than 1 done in [Mat86b, Mat86a]. As a modest first step to the similar classification problem for pre-Lie algebras, we obtain here the classification of simple graded pre-Lie algebras such that
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