Tópicos de Álgebra

Fall 2014, IMPA
Instructor: Reimundo Heluani
Office: 432
Tuesdays and Thursdays 13:30-15:00 Room 228


Aula 1 11/3
Motivations: Representations of certain infinite dimensional Lie algebras, modularity of characters. Fock representation of the Heisenberg algebra.
Aula 2 13/3
Definition of a vertex algebra. Commutative vertex algebras. Locality. Example of the affine Kac-Moody currents.
Aula 3 18/3
Example: the Heisenberg vertex algebra. nth-product of fields. Local distributions. Formal distribution Lie superalgebras.
Aula 4 20/3
Example: Affine algebras and Virasoro Algebras, Locality of the distributions
Aula 5 25/3
Equivalent definitions of vertex algebras, Borcherds identity.
Aula 6 27/3
Conformal Lie algebras, examples.
Aula 7 1/4
Conformal Lie algebras, relations with formal distribution Lie algebras. Definition as a Lie^* algebra, D-modules.