Hopf quivers

2000/09/11 by Claude Cibils, Marc Rosso, Cibils, Claude +1
Computer Science · Mathematics · #16W30 #57T05 #Advanced Graph Theory Research #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16W30 #msc:57T05

paper · pdf · doi:10.48550/arxiv.math/0009106

12 pages

arxiv created 2000/09/11 · openalex publication_date 2000/09/11 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We classify graded Hopf algebras structures over path coalgebras, that is over free pointed coalgebras, using Hopf quivers which are analogous to Cayley graphs. The description involves formulas for the product besides the canonical formulas for the coproduct. This makes explicit the quantum shuffle product making use of natural elements in a Hopf bimodule having a simple "geometrical" interpretation in the quiver sense, rather than working systematically with right or left coinvariants.

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