Listar por autor "Draper-Fontanals, Cristina"
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Con ocho basta
Draper-Fontanals, Cristina
(2022)
En esta charla hablaremos de las descripciones y particularidades de los 8 hijos del grupo de Lie compacto G_2=Aut(O), o sea, de sus cocientes reductivos. La foto de familia permitirá entender mejor la relación entre ... -
Einstein connections on Lorentzian spheres
Draper-Fontanals, Cristina (2020-03-05)
A comparison between Riemannian and Lorentzian spheres as regards the existence of Einstein connections with skew-torsion -
g2 como anillo grupo torcido
Draper-Fontanals, Cristina (2024)
El objetivo es presentar la construcción del álgebra de Lie compacta excepcional g2 como un anillo grupo torcido para el grupo Z2-cubo y el anillo suma de dos copias de los números reales. El modelo es autocontenido, ... -
Graded contractions of the [formula omitted]-grading on [formula omitted]
Draper-Fontanals, Cristina; Meyer, Thomas Leenen; Sánchez-Ortega, Juana (Elsevier, 2024)
Graded contractions of the -grading on the complex exceptional Lie algebra are classified up to equivalence and up to strong equivalence. The non-toral fine -grading is highly symmetric, with all the homogeneous components ... -
Gradings on Lie Algebras: main results and tools
Draper-Fontanals, Cristina (2018-03-07)
The aim of this talk is not to provide an explicit and complete classification of the gradings on simple finite-dimensional Lie algebras, complex and real, simply because the topic is too wide. Thus, we have selected some ... -
Graduaciones y álgebras de Lie simples
Draper-Fontanals, Cristina (2014-09-22)
Esta conferencia da una panorámica sobre cómo el concepto de graduación ha ayudado a la comprensión de la estructura en el caso de las álgebras de Lie simples, a la vez que expone el estado actual de la clasificación de ... -
Inner ideals of real Lie algebras
Draper-Fontanals, Cristina (2022-01-17)
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 ... -
Inner Ideals of Real Simple Lie Algebras
Draper-Fontanals, Cristina; Meulewaeter, Jeroen (Springer, 2022-07-18)
A classification up to automorphism of the inner ideals of the real finite-dimensional simple Lie algebras is given, jointly with precise descriptions in the case of the exceptional Lie algebras. -
El más pequeño de los grupos excepcionales
Draper-Fontanals, Cristina (2017-06-26)
El más pequeño de los grupos de Lie excepcionales, G2, será pequeño pero muy polifacético. Desde su descubrimiento por parte de Killing en 1887, los investigadores han tratado de entender el papel que tienen éste y otros ... -
Maximal abelian diagonalizable groups and fine gradings on simple Lie algebras
Draper-Fontanals, Cristina (2015-08-31)
The oldest and best known grading on a (semisimple) Lie algebra is the root space decomposition with respect to a maximal torus. This is a grading by a free abelian group (the root lattice) and it is \emph{fine} in the ... -
A new family of Einstein manifolds based on nonassociative structures
Draper-Fontanals, Cristina (2019-10-28)
For each central simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous ... -
Nonassociative structures and 3-Sasakian homogeneous manifolds
Draper-Fontanals, Cristina; Draper-Fontanals, Cristina (2019-05-17)
The 3-Sasakian homogeneous spaces are certain contact manifolds whose geometric structure is very well codified in Lie theoretical terms. This fact can be used to find interesting invariant affine connections, with nice ... -
Octonions and exceptional Lie algebras
Draper-Fontanals, Cristina (2020-03-05)
It is well known that octonions (both real and complex) are very involved in the structure of the exceptional Lie algebras. We will explore several aspects of this relationship: how octonions provide models of the exceptional ... -
Odd-dimensional spheres: nabla-Einstein manifolds
Draper-Fontanals, Cristina (2014-03-24)
Utilizamos el teorema de Nomizu sobre conexiones afines invariantes para describir variedades de Riemann-Cartan en las esferas impares, vistas como cocientes de grupos unitarios. Esta técnica nos posibilita hallar para qué ... -
Simetrías en las formas reales de e6
Draper-Fontanals, Cristina (2015-02-13)
Las graduaciones finas en las 5 posibles formas reales del álgebra de Lie excepcional e6 se discuten, proprocionando construcciones explícitas de algunas de ellas, y evidencias de la no existencia en otros casos. -
The Exceptional Lie algebra G_2.
Draper-Fontanals, Cristina (2023)
The Killing-Cartan classification of finite-dimensional complex simple Lie algebras was one of the great milestones of 19th-century mathematics. According to it, there are four infinite families of classical simple Lie ... -
The exceptional Lie group G2
Draper-Fontanals, Cristina (2017-04-05)
These notes have been prepared for the Workshop on "(Non)-existence of complex structures on $\mathbb{S}^6$", to be celebrated in Marburg in March, 2017. The material is not intended to be original. It contains a survey ... -
Three-Sasakian manifolds & the conformal group
Draper-Fontanals, Cristina (2016-03-16)
En este trabajo estudiamos las conexiones afines invariantes métricas con torsión totalmente antisimétrica en las variedades 3-Sasakianas homogéneas, aprovechando el teorema de Nomizu que tralada el problema a un contexto ...