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Lie Subalgebras of Differential Operators in One Variable

  • F. J. Plaza MartínEmail author
  • C. Tejero Prieto
Article
  • 24 Downloads

Abstract

Let \(\mathrm{Witt}\) be the Lie algebra generated by the set \(\{L_i\,\vert \, i \in {{\mathbb {Z}}}\}\) and \(\mathrm{Vir}\) its universal central extension. Let \(\mathrm{Diff}(V)\) be the Lie algebra of differential operators on \(V={{\mathbb {C}}}(\!(z)\!)\), Open image in new window or \(V={{\mathbb {C}}}(z)\). We explicitly describe all Lie algebra homomorphisms from \(\mathfrak {sl}(2)\), \(\mathrm{Witt}\), and \(\mathrm{Vir}\) to \(\mathrm{Diff}(V)\), such that \(L_0\) acts on V as a first-order differential operator.

Keywords

Witt algebra Virasoro algebra representation theory differential operators 

Mathematics Subject Classification

Primary 17B68 Secondary 81R10 

Notes

Acknowledgements

The authors would like to thank the anonymous referee for the careful reading of the paper and pointing out many typos and some inaccuracies that have helped to greatly improve this work.

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Authors and Affiliations

  1. 1.Departamento de Matemáticas and IUFFyMUniversidad de SalamancaSalamancaSpain

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