References

  1. Artemovych O.D., Blackmore D., Prykarpatski A.K. Non-associative structures of commutative algebras related with quadratic Poisson brackets. Europ. J. Math. 2020, 6, 208–231. doi:10.1007/s40879-020-00398-w
  2. Artemovych O.D., Blackmore D., Prykarpatski A.K. Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems. J. Nonlinear Math. Phys. 2017, 24 (1), 41–72. doi:10.1080/14029251.2016.1274114
  3. Biyogmam G., Tchamna S., Tcheka C. From quotient trigroups to groups. Quasigroups and Related Systems 2020, 28 (1), 29–41.
  4. Bondar E.A., Zhuchok Yu.V. Semigroups of strong endomorphisms of infinite graphs and hypergraphs. Ukr. Math. J. 2013, 65 (6), 823–834. doi:10.1007/s11253-013-0820-8
  5. Burgunder E., Ronco M.O. Tridendriform structure on combinatorial Hopf algebras. J. Algebra 2010, 324 (10), 2860–2883.
  6. Chapoton F. Algèbres de Hopf des permutahèdres, associahèdres et hypercubes. Adv. Math. 2000, 150 (2), 264–275.
  7. Curien P.-L., Delcroix-Oger B., Obradović J. Tridendriform algebras on hypergraph polytopes. Algebr. Comb. 2025, 8 (1), 201–234. doi:10.5802/alco.401
  8. Foissy L. Typed binary trees and generalized dendrifom algebras. J. Algebra 2021, 586, 1–61. doi:10.1016/j.jalgebra.2021.06.025
  9. Kinyon M.K. Leibniz Algebras, Lie Racks, and Digroups. J. Lie Theory 2017, 17, 99–114.
  10. Loday J.-L. Dialgebras. In: Dialgebras and related operads. Lect. Notes Math. Springer-Verlag, Berlin. 2001, 1763, 7–66. doi:10.1007/b80864
  11. Loday J.-L., Ronco M.O. Trialgebras and families of polytopes. Contemp. Math. 2004, 346, 369–398.
  12. Loday J.-L., Ronco M.O. Hopf Algebra of the Planar Binary Trees. Adv. Math. 1998, 139 (2), 293–309.
  13. Majumdar A., Mukherjee G. Dialgebra cohomology as a G-algebra. Trans. Amer. Math. Soc. 2003, 356 (6), 2443–2457.
  14. Movsisyan Y., Davidov S., Safaryan Mh. Construction of free \(g\)-dimonoids. Algebra Discrete Math. 2014, 18 (1), 138–148.
  15. Richter B. Dialgebren, Doppelalgebren und ihre Homologie. Diplomarbeit, Universitat Bonn 1997.
  16. Salazar-Diaz O.P., Velasquez R., Wills-Toro L.A. Generalised digroups. Comm. Algebra 2016, 44 (7), 2760–2785. doi:10.1080/00927872.2015.1065841
  17. Smith J.D.H. Cayley Theorems for Loday Algebras. Results Math. 2022, 77 (218), 1–59. doi:10.1007/s00025-022-01748-8
  18. Vallette B. Manin products, Koszul duality, Loday algebras and Deligne conjecture. J. Reine Angew. Math. 2008, 620, 105–164. doi:10.1515/crelle.2008.051
  19. Zhang Y.Y., Gao X. Free Rota-Baxter family algebras and (tri)dendriform family algebras. Pac. J. Math. 2019, 301 (2), 741–766. doi:10.2140/pjm.2019.301.741
  20. Zhuchok A.V. Certain verbal congruences on the free trioid. Algebra Discrete Math. 2024, 37 (2), 287–303. doi:10.12958/adm2274
  21. Zhuchok, A.V. Structure of free strong doppelsemigroups. Commun. Algebra 2018, 46 (8), 3262–3279. doi:10.1080/00927872.2017.1407422
  22. Zhuchok A.V. Structure of relatively free trioids. Algebra Discrete Math. 2021, 31 (1), 152–166. doi:10.12958/adm1732
  23. Zhuchok A.V., Zhuchok Yul.V., Zhuchok Yu.V. Certain congruences on free trioids. Comm. Algebra 2019, 47 (12), 5471–5481. doi:10.1080/00927872.2019.1631322
  24. Zhuchok Yul.V. Decompositions of free trioids. Bull. Taras Shevchenko Nat. Univ. Kyiv. Ser.: Phys. Math. 2014, 4, 28–34.
  25. Zhuchok Yu.V. Automorphisms of the category of free dimonoids. J. Algebra 2024, 657 (1), 883–895. doi:10.1016/j.jalgebra.2024.05.039
  26. Zhuchok Yu.V. Automorphisms of the endomorphism semigroup of a free commutative \(g\)-dimonoid. Algebra Discrete Math. 2016, 21 (2), 309–324.
  27. Zhuchok Yu.V. Endomorphism semigroups of some free products. J. Math. Sci. (USA) 2012, 187 (2), 146–152. doi:10.1007/s10958-012-1057-z
  28. Zhuchok Yu.V. Free abelian trioids. Algebra Discrete Math. 2021, 32 (1), 147–160. doi:10.12958/adm1860
  29. Zhuchok Yu.V. On representations of ordered trioids by binary relations. Scient. Bull. Uzhhorod Univ. Ser.: Math. Inform. 2018, 2 (33) , 70–77. (in Ukrainian)
  30. Zhuchok Yu.V. On the determinability of free trioids by semigroups of endomorphisms. Reports of the NAS of Ukraine 2015, 4, 7–11. doi:10.15407/dopovidi2015.04.007
  31. Zhuchok Yu.V. The endomorphism monoid of a free trioid of rank 1. Algebra Univers. 2016, 76 (3), 355–366. doi:10.1007/s00012-016-0392-1
  32. Zhuchok Yu.V. The endomorphism semigroup of a free dimonoid of rank 1. Bul. Acad. Ştiinţe Repub. Mold. Mat. 2014, 76 (3), 30–37.
  33. Zhuchok Yu.V. New models for the free commutative monogenic trioid and its endomorphism monoid. Semigroup Forum 2022, 105 (2), 575–581. doi:10.1007/s00233-022-10313-2
  34. Zhuchok Yu.V., Koppitz J. Representations of ordered doppelsemigroups by binary relations. Algebra Discrete Math. 2019, 27 (1), 144–154.
  35. Zhuchok Yu.V., Pilz G.F. A new model of the free monogenic digroup. Mat. Stud. 2023, 59 (1), 12–19. doi:10.30970/ms.59.1.12-19
  36. Zhuchok Yu.V., Pilz G.F., Zhuchok A.V. On embedding groups into digroups. Algebra Discrete Math. 2024, 38 (2), 270–287. doi:10.12958/adm2364