Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Early Access, 1 - 16
https://doi.org/10.24330/ieja.1526220

Öz

Kaynakça

  • P. Alexandroff, Diskrete raume, Rec. Math. (Mat. Sbornik) N.S., 2(44)(3) (1937), 501-519.
  • M. Ayadi, Twisted pre-Lie algebras of finite topological spaces, Comm. Algebra, 50(5) (2022), 2115-2138.
  • M. Ayadi and D. Manchon, Doubling bialgebras of finite topologies, Lett. Math. Phys., 111(4) (2021), 102 (23 pp).
  • J. S. Carter, J. Scott, S. Kamada and M. Saito, Surfaces in 4-Space, Chapter 5, Springer Science and Business Media, 2012.
  • M. Elhamdadi, Distributivity in quandles and quasigroups, in Algebra, geometry and mathematical physics, Springer Proc. Math. Stat. Springer, Heidelberg, 85 (2014), 325-340.
  • M. Elhamdadi and S. Nelson, Quandles - An Introduction to the Algebra of Knots, Student Mathematical Library 74, Amer. Math. Soc., Providence, 2015.
  • F. Fauvet, L. Foissy and D. Manchon, The Hopf algebra of finite topologies and mould composition, Ann. Inst. Fourier, 67(3) (2017), 911-945.
  • L. Foissy, Twisted bialgebras, cofreeness and cointeraction, arXiv:1905.10199 [math.RA] (2019).
  • B. Ho and S. Nelson, Matrices and finite quandles, Homology Homotopy Appl., 7(1) (2005), 197-208.
  • A. Joyal, Une theorie combinatoire des series formelles, Adv. in Math, 42(1) (1981), 1-82.
  • A. Joyal, Foncteurs analytiques et especes de structures, Combinatoire enumerative (Montreal, Que., 1985/Quebec, Que., 1985), Lecture Notes in Math., 1234 (1986), 126-159.
  • D. Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra, 23(1) (1982), 37-65.
  • P. Lopes and D. Roseman, On finite racks and quandles, Comm. Algebra, 34(1) (2006), 371-406.
  • S. V. Matveev, Distributive groupoids in knot theory, Mat. Sb. (N.S.), 119(161) (1982), 78-88,
  • R. L. Rubinsztein, Topological quandles and invariants of links, J. Knot Theory Ramifications, 16(6) (2007), 789-808.
  • A. K. Steiner, The lattice of topologies: Structure and complementation, Trans. Amer. Math. Soc., 122 (1966), 379-398.
  • R. E. Stong, Finite topological spaces, Trans. Amer. Math. Soc., 123 (1966), 325-340.
  • R. Vaidyanathaswamy, Set Topology, 2nd ed. Chelsea Publishing Co., New York, 1960.
  • D. N. Yetter, Quandles and monodromy, J. Knot Theory Ramifications, 12(4) (2003), 523-541.

A twisted Hopf algebra of finite topological quandles

Yıl 2024, Early Access, 1 - 16
https://doi.org/10.24330/ieja.1526220

Öz

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure to match the double twisted bialgebra axioms is explicitly described.

Kaynakça

  • P. Alexandroff, Diskrete raume, Rec. Math. (Mat. Sbornik) N.S., 2(44)(3) (1937), 501-519.
  • M. Ayadi, Twisted pre-Lie algebras of finite topological spaces, Comm. Algebra, 50(5) (2022), 2115-2138.
  • M. Ayadi and D. Manchon, Doubling bialgebras of finite topologies, Lett. Math. Phys., 111(4) (2021), 102 (23 pp).
  • J. S. Carter, J. Scott, S. Kamada and M. Saito, Surfaces in 4-Space, Chapter 5, Springer Science and Business Media, 2012.
  • M. Elhamdadi, Distributivity in quandles and quasigroups, in Algebra, geometry and mathematical physics, Springer Proc. Math. Stat. Springer, Heidelberg, 85 (2014), 325-340.
  • M. Elhamdadi and S. Nelson, Quandles - An Introduction to the Algebra of Knots, Student Mathematical Library 74, Amer. Math. Soc., Providence, 2015.
  • F. Fauvet, L. Foissy and D. Manchon, The Hopf algebra of finite topologies and mould composition, Ann. Inst. Fourier, 67(3) (2017), 911-945.
  • L. Foissy, Twisted bialgebras, cofreeness and cointeraction, arXiv:1905.10199 [math.RA] (2019).
  • B. Ho and S. Nelson, Matrices and finite quandles, Homology Homotopy Appl., 7(1) (2005), 197-208.
  • A. Joyal, Une theorie combinatoire des series formelles, Adv. in Math, 42(1) (1981), 1-82.
  • A. Joyal, Foncteurs analytiques et especes de structures, Combinatoire enumerative (Montreal, Que., 1985/Quebec, Que., 1985), Lecture Notes in Math., 1234 (1986), 126-159.
  • D. Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra, 23(1) (1982), 37-65.
  • P. Lopes and D. Roseman, On finite racks and quandles, Comm. Algebra, 34(1) (2006), 371-406.
  • S. V. Matveev, Distributive groupoids in knot theory, Mat. Sb. (N.S.), 119(161) (1982), 78-88,
  • R. L. Rubinsztein, Topological quandles and invariants of links, J. Knot Theory Ramifications, 16(6) (2007), 789-808.
  • A. K. Steiner, The lattice of topologies: Structure and complementation, Trans. Amer. Math. Soc., 122 (1966), 379-398.
  • R. E. Stong, Finite topological spaces, Trans. Amer. Math. Soc., 123 (1966), 325-340.
  • R. Vaidyanathaswamy, Set Topology, 2nd ed. Chelsea Publishing Co., New York, 1960.
  • D. N. Yetter, Quandles and monodromy, J. Knot Theory Ramifications, 12(4) (2003), 523-541.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

Mohamed Ayadi Bu kişi benim

Dominique Manchon Bu kişi benim

Erken Görünüm Tarihi 1 Ağustos 2024
Yayımlanma Tarihi
Gönderilme Tarihi 20 Kasım 2023
Kabul Tarihi 27 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Early Access

Kaynak Göster

APA Ayadi, M., & Manchon, D. (2024). A twisted Hopf algebra of finite topological quandles. International Electronic Journal of Algebra1-16. https://doi.org/10.24330/ieja.1526220
AMA Ayadi M, Manchon D. A twisted Hopf algebra of finite topological quandles. IEJA. Published online 01 Ağustos 2024:1-16. doi:10.24330/ieja.1526220
Chicago Ayadi, Mohamed, ve Dominique Manchon. “A Twisted Hopf Algebra of Finite Topological Quandles”. International Electronic Journal of Algebra, Ağustos (Ağustos 2024), 1-16. https://doi.org/10.24330/ieja.1526220.
EndNote Ayadi M, Manchon D (01 Ağustos 2024) A twisted Hopf algebra of finite topological quandles. International Electronic Journal of Algebra 1–16.
IEEE M. Ayadi ve D. Manchon, “A twisted Hopf algebra of finite topological quandles”, IEJA, ss. 1–16, Ağustos 2024, doi: 10.24330/ieja.1526220.
ISNAD Ayadi, Mohamed - Manchon, Dominique. “A Twisted Hopf Algebra of Finite Topological Quandles”. International Electronic Journal of Algebra. Ağustos 2024. 1-16. https://doi.org/10.24330/ieja.1526220.
JAMA Ayadi M, Manchon D. A twisted Hopf algebra of finite topological quandles. IEJA. 2024;:1–16.
MLA Ayadi, Mohamed ve Dominique Manchon. “A Twisted Hopf Algebra of Finite Topological Quandles”. International Electronic Journal of Algebra, 2024, ss. 1-16, doi:10.24330/ieja.1526220.
Vancouver Ayadi M, Manchon D. A twisted Hopf algebra of finite topological quandles. IEJA. 2024:1-16.