Georgian Mathematical Journal 13 (2006), No. 4, 741--749
Copyright Heldermann Verlag 2006
Completing the Operadic Butterfly
Jean-Louis Loday
Institut de Recherche Mathématique Avancée, CNRS et Université Louis Pasteur, 7 rue R. Descartes, 67084 Strasbourg, France
loday@math.u-strasbg.fr
We complete a certain diagram (the operadic butterfly) of the categories of algebras involving Com, As, and Lie by constructing a type of algebras which have 4 generating operations and 16 relations. The associated operad is self-dual for Koszul duality.
Keywords: Non-associative algebra, operad, Koszul duality, Zinbiel algebra, Leibniz algebra.
MSC: 18D50, 17Dxx, 17A32
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