Tópicos de Álgebra
Fall 2014, IMPA
Instructor: Reimundo Heluani
Office: 432
Tuesdays and Thursdays 13:30-15:00 Room 228
- Homework 1 (Due 18/3) PDF
- Homework 2 (Due 25/3) PDF
- Homework 3 (Due 01/4) PDF
- Homework 4 (Due 08/4) PDF
- Homework 5 (Due 15/4) PDF
- Homework 6 (Due 22/4) PDF
- Homework 7 (Due 29/4) PDF
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.