RT Conference Proceedings
T1 Inner ideals of real Lie algebras
A1 Draper-Fontanals, Cristina
K1 Lie, Algebras de
K1 Cuerpos algebráicos
AB If $L$ is a Lie algebra,  a subspace $B$ of $L$ is called an \emph{inner ideal} if $[B,[B,L]]\subset B$. This notion is inspired in Jordan algebras and it dues to [1], which used it to reconstruct the geometry defined by Tits from the corresponding Chevalley group.  Soon, [2] began a sistematic study of inner ideals of Lie algebras with a view in an Artinian theory for Lie algebras (no restrictions on the dimension or on the characteristic of the field).  A good compilation from the algebraic approach can be found in the recent monograph [3].In this poster, we clasify abelian inner ideals of the finite-dimensional  simple real Lie algebras.  Note that the   classification of the abelian inner ideals of the finite-dimensional simple complex Lie algebras was previously obtained in [4], which provided a concrete description up to automorphisms of these inner ideals in terms of roots.  Both classifications are related, since clearly if $B$ is an inner ideal of a real algebra $L$, then the complexification $B^\mathbb C=B\otimes_{\mathbb R}\mathbb C$ is an inner ideal of $L^\mathbb C
YR 2022
FD 2022-01-17
LK https://hdl.handle.net/10630/23651
UL https://hdl.handle.net/10630/23651
LA eng
NO Póster
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026