p. 1 - 7 Normal Generation of Unitary Groups of Cuntz Algebras by Involutions A. Al-Rawashdeh 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. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |