Algebraic structures of $F$-manifolds via pre-Lie algebras

Abstract

We relate the operad FMan controlling the algebraic structure on the tangent sheaf of an $F$-manifold (weak Frobenius manifold) defined by Hertling and Manin to the operad PreLie of pre-Lie algebras: for the filtration of PreLie by powers of the ideal generated by the Lie bracket, the associated graded object is FMan.

7 pages, comments are welcome

Cited by in corpus (11)

• Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras
• The algebraic and geometric classification of transposed Poisson algebras
• Transposed Poisson structures
• Endofunctors and Poincaré-Birkhoff-Witt theorems
• Mirrors, Functoriality, and Derived Geometry
• Functorial PBW theorems for post-Lie algebras
• F-manifold algebras and deformation quantization via pre-Lie algebras
• F-manifold color algebras
• Three Schur functors related to pre-Lie algebras
• Quantizations of transposed Poisson algebras by Novikov deformations
• Pre-Lie analogues of Poisson-Nijenhuis structures and Maurer-Cartan equations