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Derivations on semi-simple Jordan algebras and its applications

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arxiv 1906.04552 v1 pith:QGFVWMGI submitted 2019-05-22 math.RA

Chenrui Yao , Yao Ma , Liangyun Chen This is my paper · ORCID
classification math.RA
keywords algebrasjordansemi-simplealgebracharacteristicderivationfieldtder
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abstract

In this paper, we mainly study the derivation algebras of semi-simple Jordan algebras over a field of characteristic $0$ 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 $J$, $TDer(Der(J)) = Der(Der(J)) = ad(Der(J))$ under some assumptions. Moreover, we also show that for a semi-simple Jordan algebra $J$ which has a finite basis over a field of characteristic $0$, $TDer(J) = Der(J) = Inn(J)$. This is a corollary about our theorem which concerns Jordan algebras with unit.

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