Associative realizations of the extended Snyder model
Stjepan Meljanac, S. Mignemi
Abstract
The star product usually associated with the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.
Topics & Concepts
Noncommutative geometryHopf algebraStar productRealization (probability)SpacetimeAlgebra over a fieldLorentz transformationMathematicsOrder (exchange)Star (game theory)Product (mathematics)TwistPure mathematicsCrossed productUniversal enveloping algebraQuasitriangular Hopf algebraWeyl algebraAlgebra representationPhysicsGeometryDivision algebraMathematical analysisQuantum mechanicsFinanceEconomicsStatisticsNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsAlgebraic structures and combinatorial models