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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

 

A global dimension theorem for quantized Banach algebras


Author: N. V. Volosova
Translated by: Alex Martsinkovsky
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 70 (2009).
Journal: Trans. Moscow Math. Soc. 2009, 207-235
MSC (2000): Primary 46M18; Secondary 46H05, 46J20
Published electronically: December 3, 2009
MathSciNet review: 2573641
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for a commutative quantized ( $ \stackrel{h}{\otimes}$ and $ \stackrel{o}{\otimes}$) algebra with infinite spectrum, the maximum of its left and right global homological dimensions and, as a consequence, its homological bidimension are strictly greater than one. This result is a quantum analog of the global dimension theorem of A. Ya.  Helemskii.


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Additional Information

N. V. Volosova
Affiliation: Moscow Lomonosov State University, Moscow, Russia
Email: volosova_nv@mail.ru

DOI: http://dx.doi.org/10.1090/S0077-1554-09-00174-5
PII: S 0077-1554(09)00174-5
Published electronically: December 3, 2009
Additional Notes: Supported by the RFFI (Project No. 05–01–00982 and Project No. 08–01–00867).
Article copyright: © Copyright 2009 American Mathematical Society