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

Hilden, Hugh MichaelLozano Imízcoz, María TeresaMontesinos Amilibia, José María2023-06-202023-06-202011-10-100218-216510.1142/S0218216511009224https://hdl.handle.net/20.500.14352/43832Representations 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.engOn representations of 2-bridge knot groups in quaternion algebras.journal articlehttp://www.worldscientific.com/doi/pdf/10.1142/S0218216511009224http://www.worldscientific.com/restricted access515.162.8Quaternion algebrarepresentationknot groupGeometria algebraica1201.01 Geometría Algebraica