• 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
    • 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 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 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 ...