Quiver bialgebras and monoidal categories

Volume 131 / 2013

Hua-Lin Huang, Blas Torrecillas Colloquium Mathematicum 131 (2013), 287-300 MSC: Primary 16T10; Secondary 18D10, 16G20. DOI: 10.4064/cm131-2-10

Abstract

We study bialgebra structures on quiver coalgebras and monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural bialgebra structures. This endows the category of locally nilpotent and locally finite representations of an arbitrary quiver with natural monoidal structures from bialgebras. We also obtain theorems of Gabriel type for pointed bialgebras and hereditary finite pointed monoidal categories.

Authors

  • Hua-Lin HuangSchool of Mathematics
    Shandong University
    Jinan 250100, China
    e-mail
  • Blas TorrecillasDepartment of Algebra and Analysis
    Universidad de Almería
    04071 Almería, Spain
    e-mail

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