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Non-commutative Bloch theory. An Overview | | Michael J. Gruber
; | | Date: |
19 Dec 1998 | | Journal: | J.Math.Phys. 42 (2001) 2438-2465 | | Subject: | Mathematical Physics; Operator Algebras; Spectral Theory; Quantum Algebra MSC-class: 46N50 (Primary) 47F05, 58Gxx, 58Z05, 47N50 (Secondary) | math-ph math.MP math.OA math.QA math.SP | | Abstract: | For differential operators which are invariant under the action of an abelian group Bloch theory is the tool of choice to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a non-commutative Bloch theory for elliptic operators on Hilbert C*-modules. It relates properties of C*-algebras to spectral properties of module operators such as band structure, weak genericity of cantor spectra, and absence of discrete spectrum. It applies e.g. to differential operators invariant under a projective group action, such as Schroedinger operators with periodic magnetic field. | | Source: | arXiv, math-ph/9901011 | | Services: | Forum | Review | PDF | Favorites | |
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