On the module structure of the center of hyperelliptic Krichever-Novikov algebras

Abstract

We consider the coordinate ring of a hyperelliptic curve and let g ⊗ R be the corresponding current Lie algebra where g is a finite dimensional simple Lie algebra defined over C. We give a generator and relations description of the universal central extension of g ⊗ R in terms of certain families of polynomials P k,i and Q k,i and describe how the center Ω R /dR decomposes into a direct sum of irreducible representations when the automorphism group is C 2k or D 2k .