Yıl 2024,
Early Access, 1 - 16
Mohamed Ayadi
Dominique Manchon
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
Mohamed Ayadi
Dominique Manchon
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.