On Products and Duality of Binary, Quadratic, Regular Operads

Details On Products and Duality of Binary, Quadratic, Regular Operads On Products and Duality of Binary, Quadratic, Regular Operads

2004-07-09

arxiv.org/abs/math/0407162v2

Journal of Pure and Applied Algebra, 200, (2005), 293-317

Mathematics

Rings and Algebras

22 pages

Scientific paper

10.1016/j.jpaa.2004.12.020

Since its introduction by Loday in 1995 with motivation from algebraic K-theory, dendriform dialgebras have been studied quite extensively with connections to several areas in mathematics and physics. A few more similar structures have been found recently, such as the tri-, quadri-, ennea- and octo-algebras, with increasing complexity in their constructions and properties. We consider these constructions as operads and their products and duals, in terms of generators and relations, with the goal to clarify and simplify the process of obtaining new algebra structures from known structures and from linear operators.

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