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Master's Dissertation
DOI
Document
Author
Full name
Lucas Santos de Sá
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Dias, David Pires (President)
Hess, Patricia
Lopes, Pedro Tavares Paes
Title in Portuguese
O caráter de Chern-Connes calculado em 0 cl (S 1 ) e 0 cl (S 2 )
Keywords in Portuguese
C-álgebra
Caráter de Chern-Connes
K-teoria
Abstract in Portuguese
Este trabalho busca explorar a definição dada por Connes em [Con01] do caráter de Chern para a geometria não-comutativa. Construímos os funtores K 0 e K 1 com os principais resultados para demonstrarmos a Sequência Exata de Seis Termos e a Sequência de Mayer-Vietoris. Calculamos os grupos de K-teoria de algumas álgebras de operadores pseudo-diferenciais clássicos de ordem zero. Posteriormente usamos as sequências exatas para calcular explicitamente o caráter de Chern-Connes nos C -sistemas dinâmicos.
Title in English
The Chern-Connes character calculate in 0 cl (S 1 ) and 0 cl (S 2 )
Keywords in English
C-algebra
Chern-Connes character
K-theory
Abstract in English
This work intends to explore the definition given by Connes in [Con01] of the Chern charac- ter for noncommutative geometry. We construct the functors K 0 and K 1 with the main results to demonstrate the Exact Sequence of Six Terms and the Sequence of Mayer Vietoris. We compute the K-groups of some algebras of classical zero-order pseudo-differential operators. We then use the exact sequences to explicitly calculate the Chern-Connes Character of C -dynamic systems.
 
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Publishing Date
2019-05-31
 
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