Noncommutative Geometry and Analysis
- 23 Downloads
One of the main problems of noncommutative geometry is the translation of fundamental notions of analysis, topology, and differential geometry onto the language of Banach algebras. In this paper, we present a number of results of this kind focusing the attention on the noncommutative interpretation of the notions of differential and integral. Our presentation is based on the monographs Noncommutative Geometry by A. Connes and Elements of Noncommutative Geometry by J. M. Gracia-Bondia, J. C. Varilly, and H. Figueroa.
Keywords and phrasesC∗ -algebra Dixmier trace Wodzicki residue differential graded algebra cycle Fredholm module Chern cocycle
AMS Subject Classification47L30
Unable to display preview. Download preview PDF.
- 1.A. Connes, Noncommutative Geometry, Academic Press, London–San Diego (1994).Google Scholar
- 2.J. M. Gracia-Bondia, J. C. Varilly, and H. Figueroa, Elements of Noncommutative Geometry, Birkhäuser, Boston–Basel–Berlin (2001).Google Scholar
- 3.L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin–Heidelberg (2003).Google Scholar
- 4.A. G. Sergeev, Lectures in Functional Analysis [in Russian], Steklov Mat. Inst., Moscow (2014).Google Scholar
- 5.M. E. Taylor, Pseudodifferential Operators, Princeton Math. Ser., 34, Princeton Univ. Press, Princeton, New Jersey (1981).Google Scholar