Universal central extensions of Krichever-Novikov algebras and orthogonal polynomials
Tipo
Artigo de evento
Data de publicação
2024
Periódico
Proceedings of Symposia in Pure Mathematics
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0
Autores
Dos Santos F.A.
Futorny V.
Zhao K.
Futorny V.
Zhao K.
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Resumo
© 2024 American Mathematical Society.We give a survey of the theory of the universal central extensions of superelliptic current and derivation Lie algebras of rings of meromorphic functions on Riemann surfaces. These algebras are examples of Krichever-Novikov algebras. Their universal central extensions have finite dimensional centers which defines certain recurrence relations between its elements. The families of polynomials satisfying such recurrence relations are orthogonal polynomials, classical or nonclassical depending on initial conditions. We survey all known cases for hyperelliptic curves. We also discuss recent results on superelliptic derivation Lie algebras.