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arxiv: 0909.1706 · v1 · submitted 2009-09-09 · 🧮 math-ph · hep-th· math.MP

Lie algebraic deformations of Minkowski space with Poincare algebra

classification 🧮 math-ph hep-thmath.MP
keywords minkowskisnyderspacealgebradeformationskappacoordinatesdeformed
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We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from $\kappa$-deformed Snyder to Snyder space is constructed. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and $\kappa$-Minkowski in Maggiore-type realizations are discussed.

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