English

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 22-step solvable Lie algebra without any Novikov structure. We use extensions and classical rr-matrices to construct Novikov structures on certain classes of solvable Lie algebras.

Keywords

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

R2 v1 2026-06-23T13:56:42.980Z