1301.0484 (Martin Schlichenmaier)

Lie superalgebras of Krichever-Novikov type. Almost-grading and central
extensions    [PDF]

Martin Schlichenmaier

Classically important examples of Lie superalgebras have been constructed starting from the Witt and Virasoro algebra. In this article we consider Lie superalgebras of Krichever-Novikov type. These algebras are multi-point and higher genus equivalents. The grading in the classical case is replaced by an almost-grading. The almost-grading is determined by a splitting of the set of points were poles are allowed into two disjoint subsets. With respect to a fixed splitting, or equivalently with respect to an almost-grading, it is shown that there is up to rescaling and equivalence a unique non-trivial central extension. It is given explicitly. Furthermore, a complete classification of bounded cocycles (with respect to the almost-grading) is given.

View original: http://arxiv.org/abs/1301.0484