2010/01/31 by Sabin Cautis, Joel Kamnitzer
Mathematics · #Action (physics) #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Braid #Braid group #Braid theory #Categorical variable #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie group #Representation of a Lie group #math.AG #math.RT #msc:14F05
paper · pdf · doi:10.1112/s0010437x1100724x
published as Compositio Math. 148 (2012) 464-506 · 40 pages
arxiv created 2011/07/01 · openalex publication_date 2012/01/24 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
Abstract We introduce the idea of a geometric categorical Lie algebra action on derived categories of coherent sheaves. The main result is that such an action induces an action of the braid group associated to the Lie algebra. The same proof shows that strong categorical actions in the sense of Khovanov–Lauda and Rouquier also lead to braid group actions. As an example, we construct an action of Artin’s braid group on derived categories of coherent sheaves on cotangent bundles to partial flag varieties.