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Hopf algebra structure of incidence algebras

2012/09/06 by Denneberg, Dieter
#16T15 #16T30 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1209.1229

Abstract

The incidence algebra of a partially ordered set (poset) supports in a natural way also a coalgebra structure, so that it becomes a m-weak bialgebra even a m-weak Hopf algebra with Möbius function as antipode. Here m-weak means that multiplication and comultiplication are not required to be coalgebra- or algebra-morphisms, respectively. A rich theory is obtained in computing modulo an equivalence relation on the set of intervals in the poset.

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