Talk: Symmetrization map, realizations and Lie algebroids
Place and time: ESI, Vienna, October 14, 2010, 15:00–16:00, program Higher structures in mathematics and physics Sep-Oct 2010, organizers A. Alekseev, H. Bursztyn, T. Strobl
Abstract: In the last decade, several physicists (Amelino-Camelia, Lukierski, Wess, Meljanac, Aschieri…) studied systematically formalisms for QFT on noncommutative space-times of Lie algebra type, especially so called kappa deformations. Our work with Meljanac in Zagreb is based on realizations of noncommutative coordinates and momenta via formal differential operators having nice Hopf algebraic properties. In search for an extension of these methods to Lie algebroids, one faces the problem that the symmetrization map for the universal enveloping of a Lie algebroid is not compatible with the comultiplication. However, G. Sharygin has devised a procedure to correct the symmetrization map in the case when a global connection exists. I will present highlights of the realization method in Lie algebra case from earlier work with Meljanac, and ideas of our joint work in progress with Sharygin aimed at a generalization of the methods with realizations to Lie algebroids.
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