Classical r-matrices and Novikov algebras
Rings and Algebras
2020-03-02 v1
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 -step solvable Lie algebra without any Novikov structure. We use extensions and classical -matrices to construct Novikov structures on certain classes of solvable Lie algebras.
Cite
@article{arxiv.2002.12358,
title = {Classical r-matrices and Novikov algebras},
author = {Dietrich Burde},
journal= {arXiv preprint arXiv:2002.12358},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:math-ph/0502008