Quadri-algebras |
| |
Authors: | Marcelo Aguiar Jean-Louis Loday |
| |
Institution: | a Department of Mathematics, Texas A&M University, College Station, TX 77843, USA b Institut de Recherche Mathématique Avancée, CNRS et Université Louis Pasteur, 7 rue R. Descartes, 67084 Strasbourg, Cedex, France |
| |
Abstract: | We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner. We present several examples of quadri-algebras: the algebra of permutations, the shuffle algebra, tensor products of dendriform algebras. We show that a pair of commuting Baxter operators on an associative algebra gives rise to a canonical quadri-algebra structure on the underlying space of the algebra. The main example is provided by the algebra of linear endomorphisms of an infinitesimal bialgebra A. This algebra carries a canonical pair of commuting Baxter operators: and , where ∗ denotes the convolution of endomorphisms. It follows that is a quadri-algebra, whenever A is an infinitesimal bialgebra. We also discuss commutative quadri-algebras and state some conjectures on the free quadri-algebra. |
| |
Keywords: | 17A30 18D50 |
本文献已被 ScienceDirect 等数据库收录! |
|