q-Euclidean space and quantum group wick rotation by twisting

Abstract

We study the quantum matrix algebra $R_{21}{x}_1{x}_2=x_2{x}_{1}R$ and for the standard $2\times 2$ case propose it for the co-ordinates of $q$-deformed Euclidean space. The algebra in this simplest case is isomorphic to the usual quantum matrices $M_q(2)$ but in a form which is naturally covariant under the Euclidean rotations $S{U}_q(2)\otimes S{U}_q(2)$. We also introduce a quantum Wick rotation that twists this system precisely into the approach to $q$-Minkowski space based on braided-matrices and their associated spinorial $q$-Lorentz group.

16 pages

References in corpus (5)

• Braided Momentum Structure of the q-Poincare Group
• Quantum and Braided Linear Algebra
• Braided Matrix Structure of $q$-Minkowski Space and $q$-Poincare Group
• Cross Product Quantisation, Nonabelian Cohomology And Twisting Of Hopf Algebras
• On the Addition of Quantum Matrices

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• The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations
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• On the physical contents of q-deformed Minkowski spaces
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• Meaning of Noncommutative Geometry and the Planck-Scale Quantum Group
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• Some remarks on the {$q$}-Poincare algebra in R-matrix form
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• q-Deformed quaternions and su(2) instantons
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• Some Comments on Bosonisation and Biproducts
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• q-Quaternions and deformed su(2) instantons on the quantum Euclidean space R_q^4
• Semidual Kitaev lattice model and tensor network representation
• Construction of Cocycle Bicrossproducts by Twisting
• Yetter--Drinfeld structures on Heisenberg doubles and chains
• Quasi-{$\ast$} Structure on {$q$}-Poincare algebras