Abstract

July 1 - 17.40-18.10
D. P.K. Ghikas - Killing Symmetries in Information Geometry

We address the question concerning the possible interpretation and usefulness of the existence of Killing Symmetries of Information Manifolds, both classical and quantum. These symmetries are isometries under the action of Lie Transport on the Fisher Information metric. In the classical case we conjecture that they are related to the Transformation models of Barndorff-Nielsen while in the quantum case we expect them to be related to isoentropic transformations. As first results towards a general proof we show that for the normal family the Killing symmetry is generated by sl(2,R) , which is in fact the symmetry of the hyperbolic geometry of this family, while for two models of quantum information geometry, the SO(3) and SL(2,R) of Nencka and Streater these isometries give the isoentropic directions. Finally we discuss some possible applications of these results.

References :

1. M.K. Murray, J.W. Rice :"Differential Geometry and Statistics"
2. H. Nencka, R.F. Streater : "Information Geometry for some Lie Algebras", Infinite-Dimensional Analysis, Quantum Probability and Related Topics, 2, pp 441-460. World Scientific.
3. B. Schutz : " Geometrical Methods of Mathematical Physics"