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CMFD, 2016, Volume 59, Pages 192–200 (Mi cmfd293)  

Magnetic Schrödinger operator from the point of view of noncommutative geometry

A. G. Sergeev

Steklov Mathematical Institute, Moscow, Russia

Abstract: We give an interpretation of magnetic Schrödinger operator in terms of noncommutative geometry. In particular, spectral properties of this operator are reformulated in terms of $C^*$-algebras. Using this reformulation, one can employ the machinery of noncommutative geometry, such as Hochschild cohomology, to study the properties of magnetic Schrödinger operator. We show how this idea can be applied to the integer quantum Hall effect.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00622
Ministry of Education and Science of the Russian Federation НШ-2928.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations


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Document Type: Article
UDC: 517.984.5

Citation: A. G. Sergeev, “Magnetic Schrödinger operator from the point of view of noncommutative geometry”, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, CMFD, 59, PFUR, M., 2016, 192–200

Citation in format AMSBIB
\Bibitem{Ser16}
\by A.~G.~Sergeev
\paper Magnetic Schr\"odinger operator from the point of view of noncommutative geometry
\inbook Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22--29, 2014). Part~2
\serial CMFD
\yr 2016
\vol 59
\pages 192--200
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd293}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3545772}


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