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Flat connected finite quandles


Authors: Yoshitaka Ishihara and Hiroshi Tamaru
Journal: Proc. Amer. Math. Soc. 144 (2016), 4959-4971
MSC (2010): Primary 53C35, 57M25
Published electronically: April 25, 2016
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Abstract: Quandles can be regarded as generalizations of symmetric spaces. In the study of symmetric spaces, the notion of flatness plays an important role. In this paper, we define the notion of flat quandles, by referring to the theory of Riemannian symmetric spaces, and classify flat connected finite quandles.


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Additional Information

Yoshitaka Ishihara
Affiliation: Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Hiroshi Tamaru
Affiliation: Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
Email: tamaru@math.sci.hiroshima-u.ac.jp

DOI: https://doi.org/10.1090/proc/13095
Keywords: Quandles, symmetric spaces, flat, quandle triplets
Received by editor(s): October 5, 2015
Received by editor(s) in revised form: January 10, 2016
Published electronically: April 25, 2016
Additional Notes: The second author was supported in part by KAKENHI (24654012, 26287012).
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society