Spectra for solvable Lie algebras of bundle endomorphisms |
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Authors: | Daniel Beltiţa |
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Institution: | (1) Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO 70700 Bucharest, Romania (e-mail: dbeltita@imar.ro) , RO |
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Abstract: | The aim of the paper is to investigate spectral properties of the Lie algebras corresponding to the symmetry groups of certain
flags of vector bundles over a compact space. Under natural hypotheses, such Lie algebras are solvable, being in general infinite
dimensional. The spectral theory of finite-dimensional solvable Lie algebras of operators is extended to this natural class
of infinite-dimensional solvable Lie algebras. The discussion uses the language of continuous fields of -algebras. The flag manifolds in -algebraic framework are naturally involved here, they providing the basic method for obtaining flags of vector bundles.
Received: 8 October 2001 / Revised version: 4 February 2002 / Published online: 6 August 2002
Research supported from the contract ICA1–CT–2000–70022 with the European Commission. |
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Keywords: | Mathematics Subject Classification (2000): 47A13 22E65 58B25 46L10 |
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