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Krichever-Novikov algebras and their representations. (English) Zbl 1104.17015
Fuchs, Jürgen (ed.) et al., Noncommutative geometry and representation theory in mathematical physics. Satellite conference to the fourth European congress of mathematics, July 5–10, 2004, Karlstad, Sweden. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3718-4/pbk). Contemporary Mathematics 391, 313-321 (2005).
Krichever-Novikov algebras are two-dimensional algebraic-geometrical counterparts of Virasoro and Kac-Moody algebras. This paper is a concise survey about representations of Krichever-Novikov algebras, with the main emphasis made on fermion representations, which form a class of geometrically defined representations. The author also presents the Sugawara construction, description of quadratic Casimirs and the orbital theory for affine Krichever-Novikov algebras.
For the entire collection see [Zbl 1078.17001].
##### MSC:
 17B65 Infinite-dimensional Lie (super)algebras 17B81 Applications of Lie (super)algebras to physics, etc. 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations