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We continue analysis of \cite{Parsa:2018kys} and study rigidity and stabilityof the BMS4 algebra and its centrally extended version. We construct andclassify the family of algebras which appear as deformations of BMS4 and ingeneral find the four-parameter family of algebras W(a,b;\bar{a},\bar{b}) as aresult of the stabilization analysis, where BMS4=W(-1/2,-1/2;-1/2,-1/2). Wethen study the W(a,b;\bar{a},\bar{b}) algebra, its maximal finite subgroups andstability for different values of the four parameters. We prove stability ofthe W(a,b;\bar{a},\bar{b}) family of algebras for generic values of theparameters. For special cases of (a,b)=(\bar{a},\bar{b})=(0,0) and(a,b)=(0,-1), (\bar{a},\bar{b})=(0,0) the algebra can be deformed. Inparticular we show that centrally extended W(0,-1;0,0) algebra can be deformedto an algebra which has three copies of Virasoro as a subalgebra. We brieflydiscuss these deformed algebras as asymptotic symmetry algebras and thephysical meaning of the stabilization and implications of our result.

BMS4 Algebra, Its Stability and Deformations