Planar Carrollian statistical physics is well-defined thanks to central extensions and rotation, yielding logarithmic entropy scaling with disc area and two-dimensional ideal-gas pressure.
Central Extensions of the Quasi-orthogonal Lie algebras
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abstract
We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as well as a large number of other non-semisimple algebras, all of which have at least a semidirect structure (in some cases two or more). The dimensions of their second cohomology groups H^2(G,R) and the explicit expression of their central extensions are given.
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Statistical Physics of Planar Carroll Systems
Planar Carrollian statistical physics is well-defined thanks to central extensions and rotation, yielding logarithmic entropy scaling with disc area and two-dimensional ideal-gas pressure.