## Rocky Mountain Journal of Mathematics

### On the structure of split involutive Lie algebras

#### Abstract

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

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

Dates
First available in Project Euclid: 1 January 2015

https://projecteuclid.org/euclid.rmjm/1420071549

Digital Object Identifier
doi:10.1216/RMJ-2014-44-5-1445

Mathematical Reviews number (MathSciNet)
MR3295637

Zentralblatt MATH identifier
1343.17015

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1420071549

#### References

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