String branchings and complex tori and algebraic representations of generalized Krichever-Novikov algebras

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b-c systems. The defining cocycle for this central extension deforms to the well known Virasoro cocycle for certain kinds of degenerations of the torus. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40