Reference : Lie superalgebras of Krichever-Novikov type
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Physical, chemical, mathematical & earth Sciences : Mathematics
Lie superalgebras of Krichever-Novikov type
Schlichenmaier, Martin mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] Superalgebra ; Krichever--Novikov type algebra ; central extensions
[en] Classically,
starting from the Witt and Virasoro
important examples of
Lie superalgebras
were constructed.
In this write-up of a talk presented at the
Bia\l owie\.za meetings we report on results
on Lie superalgebras of
Krichever-Novikov type.
These algebras are multi-point and higher genus equivalents
of the classical algebras.
The grading in the classical case is replaced by an almost-grading.
It is induced
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 a fixed
almost-grading, it is shown
that there is up to rescaling and equivalence a unique
non-trivial central extension
of the Lie superalgebra of Krichever--Novikov type. It is given explicitly.
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