Introduction to Categorification (January 6–17, 2014)

Winter School I, New Directions in Lie Theory

Syllabus

Date Notes Sections Material Recommended Exercises
Jan 6
10am
1.1, 1.2 Associative algebras and their modules, finite-dimensional algebras 1.1.1, 1.1.2, 1.2.1, 1.2.2
Jan 6
2pm
2.1, 2.2 Grothendieck groups, functors 2.1.1, 2.2.1, 2.2.2
Jan 8
10am
2.3, 3.1, 3.2 Weak categorification, the Weyl algebra, the nilcoxeter algebras and their modules 2.3.1, 2.3.2, 3.2.1
Jan 9
10am
3.3 Categorification of the polynomial representation of the Weyl algebra 3.3.1, 3.3.2
Jan 13
10am
4.1, 4.2 Categorification of the Hopf algebra of symmetric functions 4.2.1
Jan 13
2pm
4.3–4.5 Categorification of the Fock space representation of the Heisenberg algebra 4.3.1, 4.4.1, 4.4.2
Jan 15
10am
5.1–5.3 Strong categorification 5.1.1, 5.3.1
Jan 16
10am
5.4–5.6 Strong categorification of the Heisenberg algebra, further directions 5.4.1

Notes

Lecture notes are posted below.