Indecomposable racks of order p2
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 s...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2004
|
| Acceso en línea: | Registro en Scopus Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 05278caa a22005297a 4500 | ||
|---|---|---|---|
| 001 | PAPER-4703 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203416.0 | ||
| 008 | 190411s2004 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-8744276582 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Graña, M. | |
| 245 | 1 | 0 | |a Indecomposable racks of order p2 |
| 260 | |c 2004 | ||
| 270 | 1 | 0 | |m Graña, M.; Depto. de Matemática, FCEyN - UBA Pab. I, Ciudad Universitaria, 1428-Buenos Aires, Argentina; email: matiasg@math.mit.edu |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a 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 | ||
| 504 | |a Burnside, W., (1955) Theory of Groups of Finite Order. 2nd Edition, , Dover Pub., New York. Zbl 0064.25105 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a Dehornoy, P., Braids and self-distributivity (2000) Progress in Mathematics, 192. , Birkhäuser Verlag, Basel. Zbl 0958.20033 | ||
| 504 | |a Etingof, P., Graña, M., On rack cohomology (2003) J. Pure Appl. Algebra, 177 (1), pp. 49-59. , Zbl pre01878448 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a Fenn, R., Rourke, C., Racks and links in codimension two (1992) J. Knot Theory Ramifications, 1 (4), pp. 343-406. , Zbl 0787.57003 | ||
| 504 | |a Graña, M., On Nichols algebras of low dimension (2000) Contemp. Math., 267, pp. 111-134. , New Trends in Hopf Algebra Theory. Zbl 0974.16031 | ||
| 504 | |a Graña, M., Quandle knot invariants are quantum knot invariants (2002) J. Knot Theory Ramifications, 11 (5), pp. 673-681. , Zbl 1027.57014 | ||
| 504 | |a Joyce, D., Classifying, A., Invariant of knots, the knot quandle (1982) J. Pure Appl. Alg., 23, pp. 37-65. , Zbl 0474.57003 | ||
| 504 | |a Kauffman, L.H., (1991) Knots and Physics, , World Scientific Pub. Co. (1994). Zbl 0868.57001 Zbl pre01666800 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a Litherland, R., Quadratic Quandles and Their Link Invariants, , Preprint available at math. GT/0207099 | ||
| 504 | |a Matveev, S.V., Distributive groupoids in knot theory (1982) Mat. Sb. Nov. Ser., 119 (1-161), pp. 78-88. , Zbl 0523.57006 | ||
| 504 | |a Mochizuki, T., Some Calculations of Cohomology Groups of Alexander Quandles, , http://math01.sci.osaka-cu.ac.jp/~takuro, Preprint available | ||
| 504 | |a Ohtsuki, T., Problems on Invariants in Knots and 3-manifolds, , http://www.is.titech.ac.jp/~tomotada/proj01/problem.ps, Preprint available | ||
| 504 | |a 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 | ||
| 504 | |a Turaev, V., Homotopy Field Theory in Dimension 3 and Crossed Group-Categories, , math. GT/0005291 | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a MIT, Mathematics Department, 77 Mass. Ave., Cambridge, MA 02139, United States | ||
| 593 | |a Depto. de Matemática, FCEyN - UBA Pab. I, Ciudad Universitaria, 1428-Buenos Aires, Argentina | ||
| 773 | 0 | |d 2004 |g v. 45 |h pp. 665-676 |k n. 2 |p Beitr. Algebr. Geom. |x 01384821 |t Beitrage zur Algebra und Geometrie | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-8744276582&partnerID=40&md5=35cca7a9f684e05db16a6b8c1fa4c44e |y Registro en Scopus |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_01384821_v45_n2_p665_Grana |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v45_n2_p665_Grana |y Registro en la Biblioteca Digital |
| 961 | |a paper_01384821_v45_n2_p665_Grana |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 65656 | ||