Gröbner Bases for Operads
نویسنده
چکیده
We define a new monoidal category on collections (shuffle composition). Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of symmetric operads. For this category, we develop the machinery of Gröbner bases for operads, and present operadic versions of Bergman’s Diamond Lemma and Buchberger’s algorithm. This machinery can be applied to study symmetric operads. In particular, we obtain an effective algorithmic version of Hoffbeck’s PBW criterion of Koszulness for (symmetric) quadratic operads.
منابع مشابه
Freeness Theorems for Operads via Gröbner Bases
We show how to use Gröbner bases for operads to prove various freeness theorems: freeness of certain operads as nonsymmetric operads, freeness of an operad Q as a P-module for an inclusion P ֒→ Q, freeness of a suboperad. This gives new proofs of many known results of this type and helps to prove some new results.
متن کاملImplementing Gröbner bases for operads
We present an implementation of the algorithm for computing Gröbner bases for operads due to the first author and A. Khoroshkin. We discuss the actual algorithms, as well as the choices made for the implementation platform and the data representation. We indicate strengths and weaknesses of our approach, and discuss possible directions for expanding the current work.
متن کاملMATH536A Paper: Gröbner Bases
An introduction to Gröbner bases and some of their uses in affine algebraic geometry.
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تاریخ انتشار 2009