Abstract
In a recent paper [9], Norberto Salinas proved that the closed subset P of all hermitian idempotents of a unital C*-algebra A is a real analytic manifold, and studied some of its geometrical properties. This space, called the Grassmann manifold of A, has a simple alternative description. There is a bijective correspondence from P to the set of all unitary representations of the cyclic group Z/2 in A. More precisely, each hermitian idempotent e in A corresponds to a representation a of Z/2 = {0,1} in A, uniquely defined by α(1) = 1 – 2e.
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© 1990 Birkhäuser Verlag Basel
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Martin, M. (1990). Projective Representations of Compact Groups in C*-Algebras. In: Helson, H., Sz.-Nagy, B., Vasilescu, FH., Arsene, G. (eds) Linear Operators in Function Spaces. Operator Theory: Advances and Applications, vol 43. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7250-8_17
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DOI: https://doi.org/10.1007/978-3-0348-7250-8_17
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