The Poincaré half-space of a C*-algebra

CORACH, GUSTAVO; RECHT, LÁZARO; ANDRUCHOW, ESTEBAN

REVISTA MATEMATICA IBEROAMERICANA

UNIV AUTONOMA MADRID

Lugar: Madrid; Año: 2019 vol. 35 p. 2187 - 2219

0213-2230

Let A be a unital C*-algebra. Given a faithful representation in a Hilbert space L, the set G^+ of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group $G$ of $a$, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the {it Poincaré half-space} H of A.