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.
Highlights
Parameters of the theory which keep the action or Hamiltonian invariant and, Noether theorem states how to associate a conserved charge to each symmetry
There is a similar notion in three dimensional (3d) flat space [35], on which we mainly focus in this paper, and is denoted by bms3. bms3 is the central extension of the bms3 [34, 36, 37]
All finite dimensional semisimple Lie algebras are rigid in the sense that they do not admit any deformation so they can be viewed as symmetry algebras of a more fundamental or an undeformed physical theory
Summary
We review the structure of asymptotic symmetry algebras appearing in the context of 3d gravity. The centerless asymptotic symmetry algebra of 3d flat spacetime is bms3 [35, 36]: i[Jm, Jn] = (m − n)Jm+n, i[Jm, Pn] = (m − n)Pm+n, i[Pm, Pn] = 0,. The asymptotic symmetry analysis of 3d flat space leads to centrally extended version of the algebra, denoted by bms: i[Jm, Jn]. The central part, besides the m3 piece, may have a piece proportional to m This latter can be absorbed in a proper redefinition of the generators, in our analysis we only include the m3 term. For flat space there are “more relaxed” boundary conditions which yield algebras with more number of fields in the various representations of the Virasoro algebra, the most general being iso(2, 1) Kac-Moody current algebra [44]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
