The composition monoid and the composition algebra at q=0 of the Kronecker quiver

2003/09/30 by Andrew Hubery, Hubery, Andrew
Mathematics · #16G20 #17B37 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Composition (language) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Kronecker delta #Linguistics #Mathematics #Monoid #Philosophy #Physics #Pure mathematics #Quantum Algebra (math.QA) #Quiver #Representation Theory (math.RT) #math.QA #math.RT #msc:16G20 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0309476

arxiv created 2003/09/30 · openalex publication_date 2003/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the Kronecker quiver and determine the relations for the specialisation to q=0 of the generic composition algebra as well as those for Reineke's composition monoid. We also obtain a normal form for the varieties occurring in the composition monoid in terms of Schur roots.

Citations

• Hall algebras and quantum groups
• Representation Theory of Artin Algebras

Related

• The Hall algebra and the composition monoid
• The composition algebra of an affine quiver
• Quivers of stylic algebras
• The monoid of families of quiver representations
• The Hall algebra of a cyclic quiver at q=0