Artículo
Graña, M. "Indecomposable racks of order p2" (2004) Beitrage zur Algebra und Geometrie. 45(2):665-676
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Abstract:
We classify indecomposable racks of order p2 (p a prime). There are 2p2-2p-2 isomorphism classes, among which 2p2-3p-1 correspond to quandles. In particular, we prove that an indecomposable quandle of order p2 is affine. As an ingredient of the classification, we prove that the quandle non-abelian second cohomology set of an indecomposable quandle of prime order is trivial.
Registro:
| Documento: | Artículo |
| Título: | Indecomposable racks of order p2 |
| Autor: | Graña, M. |
| Filiación: | MIT, Mathematics Department, 77 Mass. Ave., Cambridge, MA 02139, United States Depto. de Matemática, FCEyN - UBA Pab. I, Ciudad Universitaria, 1428-Buenos Aires, Argentina |
| Año: | 2004 |
| Volumen: | 45 |
| Número: | 2 |
| Página de inicio: | 665 |
| Página de fin: | 676 |
| Título revista: | Beitrage zur Algebra und Geometrie |
| Título revista abreviado: | Beitr. Algebr. Geom. |
| ISSN: | 01384821 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v45_n2_p665_Grana |
Referencias:
- Andruskiewitsch, N., Graña, M., From racks to pointed Hopf algebras (2003) Adv. Math., 178 (2), pp. 177-243. , Also in math. QA/0202084 Zbl 1032.16028
- Burnside, W., (1955) Theory of Groups of Finite Order. 2nd Edition, , Dover Pub., New York. Zbl 0064.25105
- Brieskorn, E., Automorphic sets and braids and singularities (1988) Contemp. Math., 78, pp. 45-115. , Braids (Santa Cruz, CA, 1986), Amer. Math. Soc., Providence, RI. Zbl 0716.20017
- Carter, J.S., Jelsovsky, D., Kamada, S., Langford, L., Saito, M., State-sum invariants of knotted curves and surfaces from quandle cohomology (1999) Electron. Res. Announc. Amer. Math. Soc., 5, pp. 146-156. , (electronic). Also in math. GT/9903135. Zbl 0995.57004
- Dehornoy, P., Braids and self-distributivity (2000) Progress in Mathematics, 192. , Birkhäuser Verlag, Basel. Zbl 0958.20033
- Etingof, P., Graña, M., On rack cohomology (2003) J. Pure Appl. Algebra, 177 (1), pp. 49-59. , Zbl pre01878448
- Etingof, P., Guralnick, R., Soloviev, A., Indecomposable set-theoretical solutions to the Quantum Yang-Baxter Equation on a set with prime number of elements (2001) J. Algebra, 242, pp. 709-719. , Zbl 1018.17007
- Etingof, P., Schedler, T., Soloviev, A., Set-theoretical solutions to the quantum Yang-Baxter equation (1999) Duke Math. J., 100 (2), pp. 169-209. , Zbl 0969.81030
- Fenn, R., Rourke, C., Racks and links in codimension two (1992) J. Knot Theory Ramifications, 1 (4), pp. 343-406. , Zbl 0787.57003
- Graña, M., On Nichols algebras of low dimension (2000) Contemp. Math., 267, pp. 111-134. , New Trends in Hopf Algebra Theory. Zbl 0974.16031
- Graña, M., Quandle knot invariants are quantum knot invariants (2002) J. Knot Theory Ramifications, 11 (5), pp. 673-681. , Zbl 1027.57014
- Joyce, D., Classifying, A., Invariant of knots, the knot quandle (1982) J. Pure Appl. Alg., 23, pp. 37-65. , Zbl 0474.57003
- Kauffman, L.H., (1991) Knots and Physics, , World Scientific Pub. Co. (1994). Zbl 0868.57001 Zbl pre01666800
- Lu, J.-H., Yan, M., Zhu, Y.-C., On the set-theoretical Yang-Baxter equation (2000) Duke Math. J., 104 (1), pp. 1-18. , Zbl 0960.16043
- Lu, J.-H., Yan, M., Zhu, Y.-C., Quasi-triangular structures on Hopf algebras with positive bases (2000) Contemp. Math., 267, pp. 339-356. , New trends in Hopf algebra theory (La Falda, 1999), Amer. Math. Soc., Providence, RI. Zbl 0978. 16034
- Litherland, R., Quadratic Quandles and Their Link Invariants, , Preprint available at math. GT/0207099
- Matveev, S.V., Distributive groupoids in knot theory (1982) Mat. Sb. Nov. Ser., 119 (1-161), pp. 78-88. , Zbl 0523.57006
- Mochizuki, T., Some Calculations of Cohomology Groups of Alexander Quandles, , http://math01.sci.osaka-cu.ac.jp/~takuro, Preprint available
- Ohtsuki, T., Problems on Invariants in Knots and 3-manifolds, , http://www.is.titech.ac.jp/~tomotada/proj01/problem.ps, Preprint available
- Soloviev, A., Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation (2000) Math. Res. Lett., 7 (5-6), pp. 577-596. , Zbl 01585085
- Turaev, V., Homotopy Field Theory in Dimension 3 and Crossed Group-Categories, , math. GT/0005291
Citas:
---------- APA ----------
(2004) . Indecomposable racks of order p2. Beitrage zur Algebra und Geometrie, 45(2), 665-676.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v45_n2_p665_Grana [ ]
---------- CHICAGO ----------
Graña, M. "Indecomposable racks of order p2" . Beitrage zur Algebra und Geometrie 45, no. 2 (2004) : 665-676.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v45_n2_p665_Grana [ ]
---------- MLA ----------
Graña, M. "Indecomposable racks of order p2" . Beitrage zur Algebra und Geometrie, vol. 45, no. 2, 2004, pp. 665-676.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v45_n2_p665_Grana [ ]
---------- VANCOUVER ----------
Graña, M. Indecomposable racks of order p2. Beitr. Algebr. Geom. 2004;45(2):665-676.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v45_n2_p665_Grana [ ]
