On products and duality of binary, quadratic, regular operads

By Kurusch Ebrahimi-Fard, Li Guo. 2004

54 citations recorded by the source corpus.

Abstract 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1ac1e532410f751eba0466b0977e0feb9a76b3bb

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Citations in the corpus

Embedding of dendriform algebras into Rota-Baxter algebras (2011, unknown): “[1, 15, 16, 38].”
On quadri-algebras (2014, methodology): “A description of Quad is given with the help of the black Manin product on nonsymmetric operads ∎, namely Quad =Dend∎Dend, where Dend is the nonsymmetric operad of dendriform algebras (this product is denoted by ◻ in [5, 11]).”
Splitting of operations, Manin products and Rota-Baxter operators (2011, methodology): “(phone) 973-353-3917;(fax) 973-353-5270. 1 2 CHENGMING BAI, OLIVIA BELLIER, LI GUO, AND XIANG NI constructions can be put into the framework of operad (black square) products for nonsymmetric operads [14, 31, 42]. By doing so, they proved that these newer algebraic structures can be obtained from th”