# ON THE STRUCTURE OF GRADED LIE TRIPLE SYSTEMS

• Published : 2016.01.31
• 68 8

#### Abstract

We study the structure of an arbitrary graded Lie triple system $\mathfrak{T}$ with restrictions neither on the dimension nor the base field. We show that $\mathfrak{T}$ is of the form $\mathfrak{T}=U+\sum_{j}I_j$ with U a linear subspace of the 1-homogeneous component $\mathfrak{T}_1$ and any $I_j$ a well described graded ideal of $\mathfrak{T}$, satisfying $[I_j,\mathfrak{T},I_k]=0$ if $j{\neq}k$. Under mild conditions, the simplicity of $\mathfrak{T}$ is characterized and it is shown that an arbitrary graded Lie triple system $\mathfrak{T}$ is the direct sum of the family of its minimal graded ideals, each one being a simple graded Lie triple system.

#### Acknowledgement

Grant : Teoria de Lie y Teoria de Espacios de Banach

Supported by : PAI, Spanish Ministerio de Educacion

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