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AUTOMORPHISMS OF NONSELFADJOINT DIRECTED GRAPH OPERATOR ALGEBRAS

Part of: Linear spaces and algebras of operators

Published online by Cambridge University Press:  09 October 2009

BENTON L. DUNCAN
BENTON L. DUNCAN*
Affiliation:
Department of Mathematics, NDSU Department 2750, PO Box 6050, Fargo ND 58108-6050, USA (email: benton.duncan@ndsu.edu)
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Abstract

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We analyze the automorphism group for the norm closed quiver algebras 𝒯+(Q). We begin by focusing on two normal subgroups of the automorphism group which are characterized by their actions on the maximal ideal space of 𝒯+(Q). To further discuss arbitrary automorphisms we factor automorphism through subalgebras for which the automorphism group can be better understood. This allows us to classify a large number of noninner automorphisms. We suggest a candidate for the group of inner automorphisms.

Keywords

graph operator algebrasautomorphisms

MSC classification

Secondary: 47L40: Limit algebras, subalgebras of $C^*$-algebras 47L55: Representations of (nonselfadjoint) operator algebras 47L75: Other nonselfadjoint operator algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 175 - 196
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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