Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.

With respect to a fixed splitting, or equivalently with respect to a fixed almost-grading, it is shown that there is up to rescaling and equivalence a unique non-trivial

As in the vector field algebra case, it will turn out that with respect to a fixed almost-grading the non-trivial almost-graded central extension (with even central element) will

One considers families of representations of the affine algebras g (which is an almost-graded cen- tral extension of g) defined over the moduli space of Riemann surfaces of genus g with

Krichever-Novikov type algebras are generalizations of the Witt, Virasoro, affine Lie algebras, and their relatives to Riemann surfaces of arbitrary genus and/or the

Krichever–Novikov type algebras are generalizations of the Witt, Virasoro, affine Lie algebras, and their relatives to Riemann surfaces of arbi- trary genus and/or the

∞). The Lie product is the same and the subalgebra can be identified with the Witt algebra W. Arbitrary genus generalizations. In the geometric setup for the Vira- soro algebra

∞). The Lie product is the same and the subalgebra can be identified with the Witt algebra W. Arbitrary genus generalizations. In the geometric setup for the Vira- soro algebra

One considers families of representations of the affine algebras b g (which is an almost-graded central extension of g) defined over the moduli space of Riemann surfaces of genus g