The p-adic quantum plane algebras and quantum Weyl algebra |
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Authors: | Bertin Diarra Fana Tangara |
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Affiliation: | (1) Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Complexe Scientifique des Cézeaux, 63177 Aubière Cedex, France;(2) Département de Mathématiques et d’Informatique, Faculté des Sciences et Techniques, Université de Bamako, B.P.E. 3206, Bamako, Mali |
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Abstract: | Let q be a principal unit of the ring of valuation of a complete valued field K, extension of the field of p-adic numbers. Generalizing Mahler basis, K. Conrad has constructed orthonormal basis, depending on q, of the space of continuous functions on the ring of p-adic integers with values in K. Attached to q there are two models of the quantum plane and a model of the quantum Weyl algebra, as algebras of bounded linear operators on the space of p-adic continuous functions. For q not a root of unit, interesting orthonormal (orthogonal) families of these algebras are exhibited and providing p-adic completion of quantum plane and quantum Weyl algebras. The text was submitted by the authors in English. |
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Keywords: | quantum plane continuous linear operators orthonormal bases continuous functions |
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