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On representations of 2-bridge knot groups in quaternion algebras.

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (2011) On representations of 2-bridge knot groups in quaternion algebras. Journal Of Knot Theory And Its Ramifications, 20 (10). p. 1419. ISSN 0218-2165

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Official URL: http://www.worldscientific.com/doi/pdf/10.1142/S0218216511009224




Abstract

Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as E3 (Euclidean 3-space), H3 (hyperbolic 3-space) and E2, 1 (Minkowski 3-space), using quaternion algebra theory, are studied. We study the different representations of a 2-generator group in which the generators are send to conjugate elements, by analyzing the points of an algebraic variety, that we call the variety of affine c-representations ofG. Each point in this variety corresponds to a representation in the unit group of a quaternion algebra and their affine deformations.


Item Type:Article
Uncontrolled Keywords:Quaternion algebra; representation; knot group
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21529
Deposited On:24 May 2013 15:40
Last Modified:12 Dec 2018 15:13

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