Reading Seminar:

Hall algebras and related topics

The seminar takes place on Monday from 10:15am - 12:00am in seminar room N 0.008.

List of talks:

The current distribution of talks is given below.

1. Introduction to Hall algebras I: Michael

  Goal: General construction of Hall algebras of finitary categories.

2. Introduction to Hall algebras II: Michael

  Goal: Hall algebras of quivers, especially the cyclic quiver

3. Crystal Hall algebra: Joanna

  Goal: Definition of generic extensions and the q=0 limit, plactic algebra and plactic relations, [R]

4. Quantum groups at roots of unity: Sondre

  Goal: tilting modules, linkage principal, tensor categories of tilting modules, negledible tilting modules, [A, AST]

5. Fusion ring of Uq(sl(n)): Arik

  Goal: Defintion of fusion ring, Verlinde formula, tensor category of tilting modules and KL-combinatorics (Soergel's Theorem), example Uq(sl(2)), [KS, AT]

6. Hall algebras a la Bridgeland: Thomas

  Goal: Construction of twisted Hall algebra, identification with quantum group, [B, P]

7. Hall algebras a la Gorsky: Olaf

  Goal: Definition of semi-derived Hall algebra, Lusztig's braid group action, [G1]

8. Semi-derived and derived Hall algebras for stable categories: Hanno

  Goal: Frobenius categories, functoriality, connection with Toen's construction, examples for existance of semi-derived but not derived version, [G2]

References:

The following is a list of references for the seminar.

[A] H.H. Andersen, Tensor products of quantized tilting modules

[AT] H.H. Andersen, D. Tubbenhauer, Diagram categories for Uq-tilting modules at roots of unity

[AST] H.H. Andersen, C. Stroppel, D. Tubbenhauer, Cellular structures using U_q tilting modules

[B] T. Bridgeland, Quantum groups via Hall algebras of complexes

[G1] M. Gorsky, Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras

[G2] M. Gorsky, Semi-derived and derived Hall algebras for stable categories

[KS] C. Korff, C. Stroppel, The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology

[P] M. Peetz, Hall Algebras via 2-periodic Complexes

[R] M. Reineke, Generic extensions and multiplicative bases of quantum groups at q=0