On the structure of graded Lie triple systems
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 163-180
https://doi.org/10.4134/BKMS.2016.53.1.163
Printed January 31, 2016
Antonio Jes\'us Calder\'on Mart\'{\i}n
Universidad de C\'{a}diz
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.
Keywords : Lie triple system, grading, simple component, structure theory
MSC numbers : Primary 17A40; Secondary 17A60, 17B70
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