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.
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Farahmand Parsa, A., Safari, H.R. & Sheikh-Jabbari, M.M. On rigidity of 3d asymptotic symmetry algebras. J. High Energ. Phys. 2019, 143 (2019). https://doi.org/10.1007/JHEP03(2019)143
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DOI: https://doi.org/10.1007/JHEP03(2019)143