Self-representations of the Möbius group
Annales Henri Lebesgue, Volume 2 (2019), pp. 259-280.


Keywords Möbius group, Lobatchevsky space, hyperbolic space, infinite-dimensional space


Contrary to the finite-dimensional case, the Möbius group admits interesting self-representations when infinite-dimensional. We construct and classify all these self-representations.

The proofs are obtained in the equivalent setting of isometries of Lobachevsky spaces and use kernels of hyperbolic type, in analogy with the classical concepts of kernels of positive and negative type.


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