Comptes Rendus
Functional Analysis
Classification of noncommutative domain algebras
[Classification des algèbres de domaines noncommutatifs]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 609-611.

Les algèbres de domaines noncommutatifs sont des analogues des algèbres de functions holomorphes sur un domaine défini par des inéquations polynômiales dans Cn. Elles généralisent également les algèbres de Hardy. Nous présentons dans cette Note la classification complète de ces algèbres, obtenue par des méthodes inspirées de lʼétude des functions biholomorphes entre domaines dʼespaces hermitiens.

Noncommutative domain algebras are noncommutative analogues of the algebras of holomorphic functions on domains of Cn defined by holomorphic polynomials, and they generalize the noncommutative Hardy algebras. We present here a complete classification of these algebras based upon techniques inspired by multivariate complex analysis, and more specifically the classification of domains in hermitian spaces up to biholomorphic equivalence.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2012.06.003

Alvaro Arias 1 ; Frédéric Latrémolière 1

1 Department of Mathematics, University of Denver, Denver, CO 80208, USA
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Alvaro Arias; Frédéric Latrémolière. Classification of noncommutative domain algebras. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 609-611. doi : 10.1016/j.crma.2012.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.06.003/

[1] A. Arias; F. Latrémolière Ergodic actions of convergent Fuchsian groups on noncommutative Hardy algebras, Proc. Amer. Math. Soc., Volume 139 (2011) no. 7, pp. 2485-2496 | arXiv

[2] A. Arias; F. Latrémolière Isomorphisms of non-commutative domain algebras, J. Oper. Theory, Volume 66 (2011) no. 2, pp. 425-450 | arXiv

[3] A. Arias, F. Latrémolière, Isomorphisms of non-commutative domains II, J. Oper. Theory (2011), 15 pp., , in press. | arXiv

[4] A. Arias; G. Popescu Noncommutative interpolation and Poisson transforms, Israel J. Math., Volume 115 (2000), pp. 205-234

[5] W. Arveson Subalgebras of C-algebras. III. Multivariable operator theory, Acta Math., Volume 181 (1998) no. 2, pp. 159-228

[6] K. Davidson; E. Katsoulis; D. Pitts The structure of free semigroup algebras, J. Reine Angew. Math., Volume 533 (2001), pp. 99-125

[7] K. Davidson; D. Pitts The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann., Volume 311 (1998), pp. 275-303

[8] K. Davidson; D. Pitts Nevanlinna–Pick interpolation for non-commutative analytic Toeplitz algebras, Integral Equations Operator Theory, Volume 31 (1998) no. 3, pp. 321-337

[9] K. Davidson; C. Ramsey; O. Shalit The isomorphism problem for some universal operator algebras, Adv. Math., Volume 228 (2011) no. 1, pp. 167-218

[10] G. Popescu Von Neumann inequality for (B(H)n)1, Math. Scand., Volume 68 (1991) no. 2, pp. 292-304

[11] G. Popescu Operator theory on noncommutative domains, Mem. Amer. Math. Soc., Volume 205 (2010) no. 954 (vi+124 pp)

[12] T. Sunada Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann., Volume 235 (1978), pp. 111-128

[13] P. Thullen Zu den Abbildungen durch analytische Funktionen mehrerer Veränderlichen, Math. Ann., Volume 104 (1931), pp. 244-259

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