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Finite-dimensional flexible algebras associated with directed and weighted CW complexes Cover

Finite-dimensional flexible algebras associated with directed and weighted CW complexes

By: Manuel Ceballos  
Open Access
|Apr 2025

References

  1. J.C. Baez, The Octonions, Bulletin of the American Mathematical Society, 39:2 (2001), 145-205.
  2. A. Carriazo, L.M. Fernández, J. Núñez, Combinatorial structures associated with Lie algebras of finite dimension, Linear Algebra Appl. 389 (2004), 43–61.
  3. A. Behn, I. Correa and I.R. Hentzel, On Flexible Algebras Satisfying x(yz) = y(zx), Algebra Colloquium, 17:1, (2010), 881–886.
  4. Y. Cabrera, M. Siles and M. V. Velasco, Evolution algebras of arbitrary dimension and their decompositions, Linear Algebra Appl. 495 (2016), 122-162.
  5. M. Ceballos, J. Núñez, A. F. Tenorio, Study of Lie algebras by using combinatorial structures, Linear Algebra Appl. 436 (2012), 349–363.
  6. M. Ceballos, J. Núñez and A.F. Tenorio, Finite-dimensional Leibniz algebras and combinatorial structures, Communications in Contemporary Mathematics 20:1 (2018), 34 pag.
  7. M. Ceballos, J. Núñez and A.F. Tenorio, Malcev Algebras and Combinatorial Structures, Applied Mathematics and Information Sciences 9, 2L (2015), 297–304.
  8. M. Ceballos, J. Núñez and A.F. Tenorio, Finite dimensional evolution algebras and (pseudo)digraphs, Mathematical Methods in the Applied Sciences DOI: 10.1002/mma.6632 (2020).
  9. M. Ceballos, J. Núñez and A.F. Tenorio, Zinbiel algebras and combinatorial structures, Analele Stiintifice ale Universitatii Ovidius Constanta. In press.
  10. A. Elduque and A. Labra, Evolution algebras and graphs, Journal of Algebra and Its Applications 14:7 (2015) 1550103, 10 pp.
  11. S. Gonzlez, Non-Associative Algebra and Its Applications. Springer, Dordrecht, 1994.
  12. F. Haray, Graph Theory. Addison-Wesley, Reading, 1969.
  13. M.N. Hounkonnou and M.L. Dassoundo, Center-symmetric algebras and bialgenras: relevant properties and consequences, Geometric Methods in Physics, XXXIV Workshop (2015), Trends in Maths., 261–273.
  14. E. Kleinfeld and L.A. Kokoris, Flexible algebras of degree one, Proc. of Amer. Math. Soc., 13:6, (1962), 891–893.
  15. F. Kosier, On a class of non-flexible algebras, Trans. of Amer. Math. Soc., 102:2, (1962), 299–318.
  16. M. Liebmann, H. Rhaak, B. Henschenmacher, Non-Associative Algebras and Quantum Physics, arXiv:1909.04027 [math-ph] (2019).
  17. J.H. Mayne, Flexible algebras of degree two, Trans. of Amer. Math. Soc. 172, (1972), 69–81.
  18. J. Núñez, M. Silvero, M.T. Villar, A particular type of non-associative algebras and graph theory, Proceedings of the 2011 international conference on Applied and computational mathematics (2011).
  19. R. H. Oehmke, On flexible algebras, Annals of Mathematics, 68:2, (1958), 221–230.
  20. M. Primc, Basic representations for classical affine Lie algebras, J. of Algebra 228 (2000), 1–50.
  21. S. Pumplün, On flexible quadratic algebras, Acta Mathematica Hungarica 119, (2007), 323–332.
  22. R.D. Schafer, On the algebras formed by the Cayley-Dickson process, American Journal of Mathematics, 76 (1954), 435–446.
  23. J.P. Serre, Algèbres de Lie Semi-Simples Complexes, Benjamin Inc., New York, 1996.
  24. J.P. Tian, Evolution algebras and their applications, Lecture Notes in Mathematics 1921, Springer, Berlin, 2008.
  25. R. Turdibaev, Bipartite graphs and the structure of finite-dimensional semisimple Leibniz algebras, International Electronic Journal of Algebra, DOI: 10.24330/ieja.587009 (2018).
  26. H.S. Wilf, Algorithms and Complexity, Prentice Hall, Englewood Cliffs, 1986.
  27. J.H.C. Whitehead, Combinatorial homotopy I, Bulletin of the American Mathematical Society 55:5 (1949), 213–245.
DOI: https://doi.org/10.2478/auom-2025-0006 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 93 - 136
Submitted on: Feb 22, 2024
Accepted on: May 15, 2024
Published on: Apr 2, 2025
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2025 Manuel Ceballos, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.