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Invariants of the half-liberated orthogonal group

Teodor Banica, Roland Vergnioux (2010)

Annales de l’institut Fourier

The half-liberated orthogonal group O n * appears as intermediate quantum group between the orthogonal group O n , and its free version O n + . We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between O n * and U n , a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that...

Isometries between groups of invertible elements in C*-algebras

Osamu Hatori, Keiichi Watanabe (2012)

Studia Mathematica

We describe all surjective isometries between open subgroups of the groups of invertible elements in unital C*-algebras. As a consequence the two C*-algebras are Jordan *-isomorphic if and only if the groups of invertible elements in those C*-algebras are isometric as metric spaces.

Isometries of the unitary groups in C*-algebras

Osamu Hatori (2014)

Studia Mathematica

We give a complete description of the structure of surjective isometries between the unitary groups of unital C*-algebras. While any surjective isometry between the unitary groups of von Neumann algebras can be extended to a real-linear Jordan *-isomorphism between the relevant von Neumann algebras, this is not the case for general unital C*-algebras. We show that the unitary groups of two C*-algebras are isomorphic as metric groups if and only if the C*-algebras are isomorphic in the sense that...

Currently displaying 621 – 640 of 1491