Advanced search
Publication Cover
Communications in Algebra Volume 49, 2021 - Issue 9
Submit an article Journal homepage
133
Views
1
CrossRef citations to date
0
Altmetric
Articles

Pre-anti-flexible bialgebras

Mafoya Landry DassoundoChern Institute of Mathematics & LPMC, Nankai University, Tianjin, ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0001-5704-7828
ORCID Icon
Pages 4050-4078 | Received 12 Jun 2020, Accepted 28 Mar 2021, Published online: 08 May 2021

References

  • Aguiar, M. (2000). Pre-Poisson algebras. Lett. Math. Phys. 54(4):263–277. DOI: 10.1023/A:1010818119040.
  • Aguiar, M. (2001). On the associative analog of Lie bialgebras. J. Algebra 244(2):492–532. DOI: 10.1006/jabr.2001.8877.
  • Bai, C. (2008). Left-symmetric bialgebras and an analogue of the classical Yang-Baxter equation. Commun. Contemp. Math. 10(02):221–260. DOI: 10.1142/S0219199708002752.
  • Bai, C. (2010). Double constructions of Frobenius algebras, Connes cocycles and their duality. J. Noncommut. Geom. 4:475–530.
  • Bai, C., Bellier, O., Guo, L., Ni, X. (2013). Spliting of operations, Manin products and Rota-Baxter operators. Int. Math. Res. Not. 2013(3):485–524. DOI: 10.1093/imrn/rnr266.
  • Baxter, G. (1960). An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. 10(3):731–742. DOI: 10.2140/pjm.1960.10.731.
  • Dassoundo, M. L., Bai, C., Hounkonnou, M. N. (2005). Anti-flexible bialgebras. arXiv: 05064.
  • Drinfeld, V. G. (1983). Hamiltonian structure on the Lie groups, Lie bialgebras and the geometric sense of the classical Yang-Baxter equations. Soviet. Math. Dokl. 27:68–71.
  • Goncharov, M. E. (2007). The classical Yang-Baxter equation on alternative algebras: The alternative D-bialgebra structure on the Cayley-Dickson matrix algebra. Sibirsk. Mat. Zh. 48:1008–1024.
  • Guo, L. (2012). An Introduction to Rota-Baxter Algebra. Surveys of Modern Mathematics. 4. Somerville, MA: International Press; Beijing: Higher Education Press.
  • Kielanowski, P., Ali, S. T., Bieliavsky, P., Odzijewicz, A., Schlichenmaier, M., Voronov, T., eds. (2016). Geometric Methods in Physics XXXIV Workshop; 2015 June 28–July 4; Białowiez. a, Poland; Trends. Maths, pp. 261–273.
  • Loday, J.-L. (2001). Dialgebras and related operads. Lecture Notes Math. 1763:7–66.
  • Pei, J., Bai, C., Guo, L. (2017). Splitting of operads and Rota-Baxter operators on operads. Appl. Categor. Struct. 25(4):505–538. DOI: 10.1007/s10485-016-9431-5.
  • Rota, G.-C. (1969). Baxter algebras and combinatorial identities I. Bull. Am. Math. Soc. 75(2):325–329. DOI: 10.1090/S0002-9904-1969-12156-7.
  • Rota, G.-C. (1969). Baxter algebras and combinatorial identities II. Bull. Am. Math. Soc. 75(2):330–334. DOI: 10.1090/S0002-9904-1969-12158-0.
  • Vinberg, E. B. (1963). Convex homogeneous cones. Tranl. Moscow. Math. Soc. 12:340–403.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.