Posets from Cancellative Operads and Koszul Duality

Abstract:

A species is said to be homogeneous concentrated in m, if for Based on previous work of Fresse [Fre04], B. Vallette [Val07] proved that a quadratic cancellative operad generated by a homogeneous species is Koszul if and only if the maximal intervals of the associated posets PQ are Cohen–Macaulay. In this chapter, we give an account of Vallete’s results and generalize his criterion for Koszulness. We show that the homogeneity assumption is not necessary. The result is still valid for any quadratic cancellative operad.

Año de publicación:

2015

Keywords:

• Cooperad
• Koszul duality
• Cohen-Macaulay Poset
• Quadratic Operad
• Linear Species

Fuente:

scopus