Functional Analysis
Classification of noncommutative domain algebras
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 609-611.

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.

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.

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DOI: 10.1016/j.crma.2012.06.003
Arias, Alvaro 1; Latrémolière, Frédéric 1

1 Department of Mathematics, University of Denver, Denver, CO 80208, USA
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Arias, Alvaro; Latrémolière, Frédéric. 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. http://www.numdam.org/articles/10.1016/j.crma.2012.06.003/

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