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The groups of automorphisms of the Witt W n and Virasoro Lie algebras

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Abstract

Let L n = K[x 1 ±1,..., x n ±1] be a Laurent polynomial algebra over a field K of characteristic zero, W n:= DerK(L n) the Lie algebra of K-derivations of the algebra L n, the so-called Witt Lie algebra, and let Vir be the Virasoro Lie algebra which is a 1-dimensional central extension of the Witt Lie algebra. The Lie algebras W n and Vir are infinite dimen- sional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: AutLie(Vir)

AutLie(W 1)

{±1}

K*, and give a short proof that AutLie(W n)

AutK-alg(L n)

GLn(Z)

K *n.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Sheffield, Hounsfield Rd, Hicks Building, Sheffield, S3 7RH, UK

    Vladimir V. Bavula

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  1. Vladimir V. Bavula
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Correspondence to Vladimir V. Bavula.

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The work is partly supported by the Royal Society and EPSRC.

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Bavula, V.V. The groups of automorphisms of the Witt W n and Virasoro Lie algebras. Czech Math J 66, 1129–1141 (2016). https://doi.org/10.1007/s10587-016-0314-6

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  • DOI: https://doi.org/10.1007/s10587-016-0314-6

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