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Normal Generation of Unitary Groups of Cuntz Algebras
Received: June 11, 2006; Accepted: January 13, 2008
Abstract. In purely infinite factors, P. de la Harpe proved that a normal subgroup of the unitary group which contains a non-trivial self-adjoint unitary contains all self-adjoint unitaries of the factor. Also he proved the same result in finite continuous factors. In a previous work the author proved a similar result in some types of unital AF-algebras. In this paper we extend the result of de la Harpe, concerning the purely infinite factors to a main example of purely infinite C*-algebras called the Cuntz algebras On(2 £ n £ ¥) and we prove that U(On) is normally generated by some non-trivial involution. In particular, in the Cuntz algebra O¥ we prove that U(O¥) is normally generated by self-adjoint unitary of odd type.
Keywords: Cuntz algebras; involutions; K-Theory.
AMS Subject classification: Primary: 46L05; 46L80.
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