Algebras and Representation Theory

, Volume 20, Issue 2, pp 433–468 | Cite as

Extending Representations of \(\mathfrak {sl}(2)\) to Witt and Virasoro Algebras

  • Francisco J. Plaza MartĂ­n
  • Carlos Tejero Prieto


We study when an \(\mathfrak {sl}(2)\)-representation extends to a representation of the Witt and Virasoro algebras. We give a criterion for extendability and apply it to certain classes of weight \(\mathfrak {sl}(2)\)-modules. For all simple weight \(\mathfrak {sl}(2)\)-modules and those in any of the abelian Krull-Schmidt categories of weight modules whose unique simple object is a dense module, we fully characterize which ones admit extensions, and we obtain explicit expressions for all of them. We also give partial results in the same direction for the abelian categories of weight modules which have two and three simple objects.


Witt algebras Virasoro algebra Partial Lie algebras Extensions of representations Simple weight modules 

Mathematics Subject Classification (2010)

17B68 81R10 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Departamento de MatemĂĄticas and IUFFYMUniversidad de SalamancaSalamancaSpain

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