Ennea-algebras

By P. Leroux. 2003

52 citations recorded by the source corpus.

We propose a generalisation of a recent work of M. Aguiar and J.-L. Loday on Quadri-algebras, called Ennea-algebras. In this second version, this paper has been extended. We show that the augmented free Ennea-algebra is a connected Hopf algebra and construct explicit formal deformations of dendriform dialgebras, quari-algebras and ennea-algebras via Baxter operators.

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

View Paper: https://www.semanticscholar.org/paper/3e1f04237fff340fba4d9f3285870e4293aff1f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Li Guo
2. Kurusch Ebrahimi-Fard
3. Chengming Bai
4. Jean-Louis Loday
5. Xianglong Ni
6. Olivia Bellier
7. William F. Keigher
8. Yuqun Chen

In Geometry and Topology

1. Li Guo
2. Kurusch Ebrahimi-Fard
3. Jean-Louis Loday
4. Chengming Bai
5. Xianglong Ni
6. Olivia Bellier
7. William F. Keigher
8. Yuqun Chen

In Mathematical Physics

1. Li Guo
2. Chengming Bai
3. Olivia Bellier
4. Xianglong Ni
5. Kurusch Ebrahimi-Fard
6. Jean-Louis Loday
7. Loïc Foissy
8. Samuele Giraudo

Citations in the corpus

• Rota–Baxter algebras and dendriform algebras (2005, background): “QA/0311132 [52] P. Leroux, On some remarkable operads constructed from Baxter operators, arXiv:math.”
• Generalized bialgebras and triples of operads (2006, background): “[47, 52, 54, 53, 3, 41, 17]) are examples of multiplicative operads with generalized associative relations.”
• Splitting of operations, Manin products and Rota-Baxter operators (2011, background): “[26] P. Leroux, On some remarkable operads constructed fromBaxter operators, arXiv: math.”
• FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, background): “Recently, there have been several interesting developments of Rota–Baxter algebras in theoretical physics and mathematics, including quantum field theory [12, 13, 43, 44, 51], associative Yang–Baxter equations [1, 2], shuffle products [18, 36, 37], operads [4, 15, 19, 45, 46], Hopf algebras [6, 18],”
• Mixable shuffles, quasi-shuffles and Hopf algebras (2005, background): “In recent years, Rota-Baxter algebras have found applications in quantum field theory [8, 9, 15, 16, 17], dendriform algebras [1, 10, 13, 31], number theory [22], Hopf algebras [2] and combinatorics [21].”