On Products and Duality of Binary, Quadratic, Regular Operads
arXiv:math/0407162 · doi:10.1016/j.jpaa.2004.12.020
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.
22 pages
References in corpus (10)
- Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
- Renormalization in quantum field theory and the Riemann-Hilbert problem II: the -function, diffeomorphisms and the renormalization group
- Loday-type Algebras and the Rota-Baxter Relation
- Integrable Renormalization II: the general case
- Mixable Shuffles, Quasi-shuffles and Hopf Algebras
- Koszul duality of operads and homology of partition posets
- Integrable Renormalization I: the Ladder Case
- On some remarkable operads constructed from Baxter operators
- On the associative Nijenhuis Relation
- The Operad Quad is Koszul
Cited by in corpus (17)
- Splitting of operations, Manin products and Rota-Baxter operators
- Rota-Baxter Algebras and Dendriform Algebras
- Integrable Renormalization II: the general case
- Mixable Shuffles, Quasi-shuffles and Hopf Algebras
- Free Rota-Baxter algebras and rooted trees
- On embedding of dendriform algebras into Rota---Baxter algebras
- Manin products, Koszul duality, Loday algebras and Deligne conjecture
- Multiple zeta values and Rota--Baxter algebras
- Twisted dendriform algebras and the pre-Lie Magnus expansion
- Completing the operadic butterfly
- Generalized shuffles related to Nijenhuis and TD-algebras
- Special identities for the pre-Jordan product in the free dendriform algebra
- Replicating of binary operads, Koszul duality, Manin products and average operators
- Coherent Unit Actions on Operads and Hopf Algebras
- Rota-Baxter Algebra. The Combinatorial Structure of Integral Calculus
- On dual quadri-algebras
- Splitting of operations for alternative and Malcev structures