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
O(2 £ _{n}n
£ ¥) and we prove that
U(O) is normally generated by some non-trivial
involution. In particular, in the Cuntz algebra
O_{n}
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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