Classification of flat connected quandles
Let A be an additive abelian group. Then the binary operation a ∗ b = 2 b − a gives a quandle structure on A , denoted by T ( A ) , and called the Takasaki quandle of A . Viewing quandles as generalization of Riemannian symmetric spaces, Ishihara and Tamaru [Flat connected finite quandles, to appear...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Singh, Mahender [verfasserIn] |
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Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © 2016, World Scientific Publishing Company |
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| Übergeordnetes Werk: |
Enthalten in: Journal of knot theory and its ramifications - Singapore [u.a.] : World Scientific, 1992, 25(2016), 13 |
|---|---|
| Übergeordnetes Werk: |
volume:25 ; year:2016 ; number:13 |
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| DOI / URN: |
10.1142/S0218216516500711 |
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| 520 | |a Let A be an additive abelian group. Then the binary operation a ∗ b = 2 b − a gives a quandle structure on A , denoted by T ( A ) , and called the Takasaki quandle of A . Viewing quandles as generalization of Riemannian symmetric spaces, Ishihara and Tamaru [Flat connected finite quandles, to appear in Proc. Amer. Math. Soc. (2016)] introduced flat quandles, and classified quandles which are finite, flat and connected. In this note, we classify all flat connected quandles. More precisely, we prove that a quandle X is flat and connected if and only if X ≅ T ( A ) , where A is a 2-divisible group. | ||
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10.1142/S0218216516500711 doi PQ20170301 (DE-627)OLC198939034X (DE-599)GBVOLC198939034X (PRQ)s1011-4dce86da592eae001a6e69aa5cecdc2ca284fd13916466f4cc0ec44e8fb0dfa80 (KEY)0215615620160000025001300000classificationofflatconnectedquandles DE-627 ger DE-627 rakwb eng 510 ZDB Singh, Mahender verfasserin aut Classification of flat connected quandles 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Let A be an additive abelian group. Then the binary operation a ∗ b = 2 b − a gives a quandle structure on A , denoted by T ( A ) , and called the Takasaki quandle of A . Viewing quandles as generalization of Riemannian symmetric spaces, Ishihara and Tamaru [Flat connected finite quandles, to appear in Proc. Amer. Math. Soc. (2016)] introduced flat quandles, and classified quandles which are finite, flat and connected. In this note, we classify all flat connected quandles. More precisely, we prove that a quandle X is flat and connected if and only if X ≅ T ( A ) , where A is a 2-divisible group. Nutzungsrecht: © 2016, World Scientific Publishing Company Enthalten in Journal of knot theory and its ramifications Singapore [u.a.] : World Scientific, 1992 25(2016), 13 (DE-627)131064819 (DE-600)1108304-9 (DE-576)033026351 0218-2165 nnns volume:25 year:2016 number:13 http://dx.doi.org/10.1142/S0218216516500711 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2409 GBV_ILN_4310 GBV_ILN_4323 AR 25 2016 13 |
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Let A be an additive abelian group. Then the binary operation a ∗ b = 2 b − a gives a quandle structure on A , denoted by T ( A ) , and called the Takasaki quandle of A . Viewing quandles as generalization of Riemannian symmetric spaces, Ishihara and Tamaru [Flat connected finite quandles, to appear in Proc. Amer. Math. Soc. (2016)] introduced flat quandles, and classified quandles which are finite, flat and connected. In this note, we classify all flat connected quandles. More precisely, we prove that a quandle X is flat and connected if and only if X ≅ T ( A ) , where A is a 2-divisible group. |
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Let A be an additive abelian group. Then the binary operation a ∗ b = 2 b − a gives a quandle structure on A , denoted by T ( A ) , and called the Takasaki quandle of A . Viewing quandles as generalization of Riemannian symmetric spaces, Ishihara and Tamaru [Flat connected finite quandles, to appear in Proc. Amer. Math. Soc. (2016)] introduced flat quandles, and classified quandles which are finite, flat and connected. In this note, we classify all flat connected quandles. More precisely, we prove that a quandle X is flat and connected if and only if X ≅ T ( A ) , where A is a 2-divisible group. |
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Let A be an additive abelian group. Then the binary operation a ∗ b = 2 b − a gives a quandle structure on A , denoted by T ( A ) , and called the Takasaki quandle of A . Viewing quandles as generalization of Riemannian symmetric spaces, Ishihara and Tamaru [Flat connected finite quandles, to appear in Proc. Amer. Math. Soc. (2016)] introduced flat quandles, and classified quandles which are finite, flat and connected. In this note, we classify all flat connected quandles. More precisely, we prove that a quandle X is flat and connected if and only if X ≅ T ( A ) , where A is a 2-divisible group. |
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