course dates credits
Differential Geometry and Group Theory Oct 4 - Oct 29 3
teachers schedule term
Francesco Benini 10:00 - 11:30 1


  • Topology
  • Differentiable manifolds: vector fields, forms, integration, Lie derivative
  • Lie groups: action of groups on manifolds, Lie algebras
  • Riemannian geometry: metric, connections, curvature, (conformal) Killing vectors
  • Lie algebras: simple and semi-simple algebras, Killing form, Cartan-Weyl basis, weights, Cartan matrix and Dynkin diagrams, classification of simple Lie algebras, Weyl group, congruence classes, low-rank examples
  • Highest-weight representations: Dynkin labels, Freudenthal multiplicity formula, Casimir operators, Dynkin index, tensor product decomposition, su(N) and Young diagrams
  • Real forms and compact Lie groups: split and compact real form
  • Spinors in various dimensions
  • Poincare' and conformal groups
  • Prerequisites:


    Online Resources:

    Filename Size (bytes) Date Modified
    SISSA_Groups_course.pdf 874.24 KB Nov 16 2021 10:18 AM