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On representations of 2-bridge knot groups in quaternion algebras II: The case of the Trefoil knot group

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (2013) On representations of 2-bridge knot groups in quaternion algebras II: The case of the Trefoil knot group. Journal Of Knot Theory And Its Ramifications, 22 (1). ISSN 0218-2165

Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0218216512501404




Abstract

The complete classification of representations of the Trefoil knot group G in S3 and SL(2, ℝ), their affine deformations, and some geometric interpretations of the results, are given. Among other results, we also obtain the classification up to conjugacy of the noncyclic groups of affine Euclidean isometries generated by two isometries μ and ν such that μ2 = ν3 = 1, in particular those which are crystallographic. We also prove that there are no affine crystallographic groups in the three-dimensional Minkowski space which are quotients of G.


Item Type:Article
Uncontrolled Keywords:Quaternion algebra; representation; knot group; crystallographic group
Subjects:Sciences > Mathematics > Group Theory
Sciences > Mathematics > Algebraic geometry
ID Code:21530
Deposited On:24 May 2013 15:41
Last Modified:12 Dec 2018 15:12

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