6533b7d6fe1ef96bd12667a6

RESEARCH PRODUCT

Categorical action of the extended braid group of affine type $A$

Agnès GadbledAnne-laure ThielAnne-laure ThielEmmanuel Wagner

subject

[ MATH ] Mathematics [math]Pure mathematicsGeneral MathematicsCategorificationBraid groupGeometric intersection01 natural sciencesMathematics - Geometric TopologyMorphismMathematics::Category TheoryQuiverMathematics - Quantum Algebra0103 physical sciencesFOS: MathematicsQuantum Algebra (math.QA)Representation Theory (math.RT)0101 mathematics[MATH]Mathematics [math]MathematicsHomotopy categoryGroup (mathematics)Applied Mathematics010102 general mathematicsQuiverBraid groupsGeometric Topology (math.GT)16. Peace & justiceCategorificationCategorical actionBounded functionMSC: 20F36 18E30 57M99 13D99010307 mathematical physicsAffine transformationMathematics - Representation Theory

description

Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.

yearjournalcountryeditionlanguage
2017-06-01
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01549167