Classical r-matrices and Novikov algebras

2020/02/27 by Dietrich Burde
Mathematics · #math.RA #msc:17B30

paper · pdf · doi:10.1007/s10711-006-9059-y

published as Geometriae Dedicata, Vol. 122, Issue 1, 145-157 (2006) · arXiv admin note: substantial text overlap with arXiv:math-ph/0502008

arxiv created 2020/02/27 · arxiv updated 2020/03/02

Abstract

We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras.

Citations

• Novikov structures on solvable Lie algebras