论文信息 - Pre-Lie algebras and the rooted trees operad

Pre-Lie algebras and the rooted trees operad

A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatorial description in terms of rooted trees of the operad associated to this type of algebras and prove that it is a Koszul operad.

F. Chapoton | M. Livernet

[1] Frédéric Chapoton,et al. Un endofoncteur de la catégorie des opérades , 2001 .

[2] C. Brouder,et al. Runge–Kutta methods and renormalization , 1999, hep-th/9904014.

[3] A. Connes,et al. Hopf Algebras, Renormalization and Noncommutative Geometry , 1998, hep-th/9808042.

[4] A. Dzhumadil'daev. Conomologies and deformations of right-symmetric algebras , 1998, math/9807065.

[5] J.-L. Loday. La renaissance des opérades , 1995 .

[6] M. Kapranov,et al. Koszul duality for Operads , 1994, 0709.1228.

[7] E. Getzler,et al. Homotopy algebra and iterated integrals for double loop spaces , 1994, hep-th/9403055.

[8] J. M. Boardman,et al. Homotopy Invariant Algebraic Structures on Topological Spaces , 1973 .

[9] J. P. May,et al. The geometry of iterated loop spaces , 1972 .

[10] Y. Matsushima. Affine structures on complex manifolds , 1968 .

[11] Murray Gerstenhaber,et al. The Cohomology Structure of an Associative Ring , 1963 .