2021/06/29 by Taric Aît Aissa, Aissa, Taric Aît, Wadia Mansouri +1
Mathematics · #17B30 #17B60 #53D05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2106.15165
openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that a symplectic Lie algebra admit a left symmetric product. In this work, we study the case where this product is Novikov, we show that the left-symmetric product associated to the symplectic Lie algrbra is Novikov if and only if it is associative. In this case the symplectic Lie algebra is called symplectic Novikov Lie algebra(SNLA). We show that any SNLA is completely reducible two-step solvable. The classification of 4-dimensional and nilpotent 6-dimensional, also some methods for building large classes of examples are presented. Finally, we give a geometric study of the affine connection associated with an SNLA.