Hostname: page-component-cb9f654ff-p5m67 Total loading time: 0 Render date: 2025-09-02T11:43:28.957Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Information

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

References

[1]Alaimia, M., ‘Automorphisms of some Banach algebras of analytic functions’, Linear Algebra Appl. 298 (1999), 87–97.CrossRefGoogle Scholar
[2]Davidson, K. and Katsoulis, E., ‘Nest representations of directed graph algebras’, Proc. Lond. Math. Soc. 92(30) (2006), 762–790.CrossRefGoogle Scholar
[3]Davidson, K. and Pitts, D., ‘The algebraic structure of non-commutative analytic Toeplitz algebras’, Math. Ann. 311(2) (1998), 275–303.CrossRefGoogle Scholar
[4]Duncan, B., ‘Finite dimensional point derivations for graph algebras’, Illinois J. Math. 52(2) (2009), 419–435.Google Scholar
[5]Katsoulis, E. and Kribs, D., ‘Isomorphisms of algebras associated with directed graphs’, Math. Ann. 330 (2004), 709–728.CrossRefGoogle Scholar
[6]Kribs, D. and Power, S., ‘Free semigroupoid algebras’, J. Ramanujan Math. Soc. 19 (2004), 75–114.Google Scholar
[7]Muhly, P., ‘A finite dimensional introduction to operator algebras’, in: Operator Algebras and Applications (SAMOS, 1996) (Kluwer Academic, Dordrecht, 1997), pp. 315–354.Google Scholar