XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

Jiri Hrivnak

Twisted Cocycles of Contracted sl(3,C)

We apply the concept of twisted cocycles to graded contractions of sl(3,C). This concept turns out to be effective tool, besides symmetry group of a grading, for distinguishing among results of graded contraction procedure. Twisted cocycles are standard cohomology cocycles generalized via certain complex parameters. The dimensionalities of spaces of such cocycles then form complex functions which are invariant under Lie isomorphisms. We present overview of solutions of contraction equations for each of four fine group gradings of sl(3,C) and show the role of twisted cocycles in the identification process. We focus on so called Gall-Mann grading and compare contraction results to earlier results from the Pauli and the Cartan grading of sl(3,C). This is joint work with P. Novotny.