Rocky Mountain Journal of Mathematics

On the structure of split involutive Lie algebras

Antonio J. Calderón Martín and José M. Sánchez Delgado

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We study the structure of arbitrary split involutive Lie algebras. We show that any of such algebras $L$ is of the form $L={\mathcal U} +\sum_{j}I_{j}$ with ${\mathcal U}$ a subspace of the involutive abelian Lie subalgebra $H$ and any $I_{j}$ a well described involutive ideal of $L$ satisfying $[I_j,I_k]=0$ if $j\neq k$. Under certain conditions, the simplicity of $L$ is characterized and it is shown that $L$ is the direct sum of the family of its minimal involutive ideals, each one being a simple split involutive Lie algebra.

Article information

Rocky Mountain J. Math., Volume 44, Number 5 (2014), 1445-1455.

First available in Project Euclid: 1 January 2015

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Zentralblatt MATH identifier

Primary: 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65] 17B20: Simple, semisimple, reductive (super)algebras 17B05: Structure theory

Infinite dimensional Lie algebras involutive Lie algebras split Lie algebras roots root spaces


Martín, Antonio J. Calderón; Delgado, José M. Sánchez. On the structure of split involutive Lie algebras. Rocky Mountain J. Math. 44 (2014), no. 5, 1445--1455. doi:10.1216/RMJ-2014-44-5-1445.

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