English

Derivations on semi-simple Jordan algebras and its applications

Rings and Algebras 2019-06-12 v1

Abstract

In this paper, we mainly study the derivation algebras of semi-simple Jordan algebras over a field of characteristic 00 and give sufficient and necessary conditions that the derivation algebras of them are simple. As an application, we prove that for a semi-simple Jordan algebra JJ, TDer(Der(J))=Der(Der(J))=ad(Der(J))TDer(Der(J)) = Der(Der(J)) = ad(Der(J)) under some assumptions. Moreover, we also show that for a semi-simple Jordan algebra JJ which has a finite basis over a field of characteristic 00, TDer(J)=Der(J)=Inn(J)TDer(J) = Der(J) = Inn(J). This is a corollary about our theorem which concerns Jordan algebras with unit.

Keywords

Cite

@article{arxiv.1906.04552,
  title  = {Derivations on semi-simple Jordan algebras and its applications},
  author = {Chenrui Yao and Yao Ma and Liangyun Chen},
  journal= {arXiv preprint arXiv:1906.04552},
  year   = {2019}
}