FINITENESS PROPERTIES FOR THE PATH COALGEBRA ASSOCIATED TO A POSET
Journal Title: Journal of Science And Arts - Year 2011, Vol 14, Issue 1
Abstract
Let P be a partially ordered set (poset) locally finite and kQ the path coalgebra over a field k associated to P. In this paper we investigate finiteness properties of this coalgebra by using an injective morphism of coalgebras from incidence coalgebra kS of P to the path coalgebra kQ. We deduce that kQ is left semiperfect only if kS have the same property, and that kQ is cosemisimple when the order relation on P is the equality. Finally we characterize the coradical filtration of the path coalgebra.
Authors and Affiliations
VELICU GEORGIANA
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