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On rigidity of 3d asymptotic symmetry algebras

  • A. Farahmand Parsa
  • H. R. SafariEmail author
  • M. M. Sheikh-Jabbari
Open Access
Regular Article - Theoretical Physics
  • 45 Downloads

Abstract

We study rigidity and stability of infinite dimensional algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider algebras appearing as asymptotic symmetries of three dimensional spacetimes, the \( \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_3 \), \( \mathfrak{u}(1) \) Kac-Moody and Virasoro algebras. We construct and classify the family of algebras which appear as deformations of \( \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_3 \), \( \mathfrak{u}(1) \) Kac-Moody and their central extensions by direct computations and also by cohomological analysis. The Virasoro algebra appears as a specific member in this family of rigid algebras; for this case stabilization procedure is inverse of the Inönü-Wigner contraction relating Virasoro to bms3 algebra. We comment on the physical meaning of deformation and stabilization of these algebras and relevance of the family of rigid algebras we obtain.

Keywords

Conformal and W Symmetry Differential and Algebraic Geometry Gaugegravity correspondence Space-Time Symmetries 

Notes

Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.School of Mathematics, Institute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.School of Mathematics, TATA Institute of Fundamental Research (TIFR)MumbaiIndia
  3. 3.School of Physics, Institute for Research in Fundamental Sciences (IPM)TehranIran

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