[Classification des algèbres de domaines noncommutatifs]
Les algèbres de domaines noncommutatifs sont des analogues des algèbres de functions holomorphes sur un domaine défini par des inéquations polynômiales dans . 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 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.
Accepté le :
Publié le :
@article{CRMATH_2012__350_11-12_609_0,
author = {Arias, Alvaro and Latr\'emoli\`ere, Fr\'ed\'eric},
title = {Classification of noncommutative domain algebras},
journal = {Comptes Rendus. Math\'ematique},
pages = {609--611},
publisher = {Elsevier},
volume = {350},
number = {11-12},
year = {2012},
doi = {10.1016/j.crma.2012.06.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.06.003/}
}
TY - JOUR AU - Arias, Alvaro AU - Latrémolière, Frédéric TI - Classification of noncommutative domain algebras JO - Comptes Rendus. Mathématique PY - 2012 SP - 609 EP - 611 VL - 350 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.06.003/ DO - 10.1016/j.crma.2012.06.003 LA - en ID - CRMATH_2012__350_11-12_609_0 ER -
%0 Journal Article %A Arias, Alvaro %A Latrémolière, Frédéric %T Classification of noncommutative domain algebras %J Comptes Rendus. Mathématique %D 2012 %P 609-611 %V 350 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.06.003/ %R 10.1016/j.crma.2012.06.003 %G en %F CRMATH_2012__350_11-12_609_0
Arias, Alvaro; Latrémolière, Frédéric. Classification of noncommutative domain algebras. Comptes Rendus. Mathématique, Tome 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/
[1] Ergodic actions of convergent Fuchsian groups on noncommutative Hardy algebras, Proc. Amer. Math. Soc., Volume 139 (2011) no. 7, pp. 2485-2496 | arXiv
[2] 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] Noncommutative interpolation and Poisson transforms, Israel J. Math., Volume 115 (2000), pp. 205-234
[5] Subalgebras of -algebras. III. Multivariable operator theory, Acta Math., Volume 181 (1998) no. 2, pp. 159-228
[6] The structure of free semigroup algebras, J. Reine Angew. Math., Volume 533 (2001), pp. 99-125
[7] The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann., Volume 311 (1998), pp. 275-303
[8] Nevanlinna–Pick interpolation for non-commutative analytic Toeplitz algebras, Integral Equations Operator Theory, Volume 31 (1998) no. 3, pp. 321-337
[9] The isomorphism problem for some universal operator algebras, Adv. Math., Volume 228 (2011) no. 1, pp. 167-218
[10] Von Neumann inequality for , Math. Scand., Volume 68 (1991) no. 2, pp. 292-304
[11] Operator theory on noncommutative domains, Mem. Amer. Math. Soc., Volume 205 (2010) no. 954 (vi+124 pp)
[12] Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann., Volume 235 (1978), pp. 111-128
[13] Zu den Abbildungen durch analytische Funktionen mehrerer Veränderlichen, Math. Ann., Volume 104 (1931), pp. 244-259
Cité par Sources :
