Braid groups and quiver mutation
| Autor: | Joseph Grant, Robert J. Marsh |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Coxeter group Quiver Braid group Group Theory (math.GR) Type (model theory) 01 natural sciences Cluster algebra Interpretation (model theory) Mathematics::Category Theory 0103 physical sciences Mutation (knot theory) FOS: Mathematics 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Mathematics - Group Theory Simple module Mathematics - Representation Theory Mathematics |
| Zdroj: | Pacific Journal of Mathematics. 290:77-116 |
| ISSN: | 1945-5844 0030-8730 |
| Popis: | We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers, building on work of Barot and Marsh for Coxeter groups. In types A and D these presentations can be understood geometrically using triangulated surfaces. We then give a categorical interpretation of the presentations, with the new generators acting as spherical twists at simple modules on derived categories of Ginzburg dg-algebras of quivers with potential. Comment: 35 pages; v2 is post referee report |
| Databáze: | OpenAIRE |
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