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- Eric Hoffbeck
- 2010

The aim of this article is to give a criterion, generalizing the criterion introduced by Priddy for algebras, to verify that an operad is Koszul. We define the notion of a Poincaré-Birkhoff-Witt… (More)

The purpose of this paper is to study generalizations of Gamma-homology in the context of operads. Good homology theories are associated to operads under appropriate cofibrancy hypotheses, but this… (More)

Several constructive homological methods based on noncommutative Gröbner bases are known to compute free resolutions of associative algebras. In particular, these methods relate the Koszul property… (More)

We define higher dimensional linear rewriting systems, called linear polygraphs, for presentations of associative algebras, generalizing the notion of noncommutative Gröbner bases. They are… (More)

We prove that Leibniz homology of Lie algebras can be described as functor homology in the category of linear functors from a category associated to the Lie operad. Mathematics Subject… (More)

- Eric Hoffbeck
- 2016

The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we… (More)

In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of being Koszul and… (More)

- Eric Hoffbeck
- 2009

- Eric Hoffbeck, Ieke Moerdijk
- Eur. J. Comb.
- 2018

We discuss a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. We give several equivalent descriptions, and prove some algebraic and combinatorial… (More)

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