K-theory for C*-algebras: The hexagonal exact sequence
Paraules clau:Operator Algebras, Non-commutative Topology, K-Theory.
ResumThe aim of this work is to introduce the reader to C*-algebraic K-theory whilst proving two of its main known results: Bott periodicity and the hexagonal exact sequence. These constitute a determinant tool for the explicit computation of the K-groups of a C*-algebra, and have been used succesfully to study a variety of families. In order to state them, we deviate slightly from the standard literature and introduce the notation K', which allows us to simplify the results and denitions needed to understand their proofs.
Keywords: Operator Algebras, Non-commutative Topology, K-Theory.MSC (2010): 46L05, 46L35, 46L80, 46L85.
Vilalta Vila, E. (2020). K-theory for C*-algebras: The hexagonal exact sequence. Reports@SCM, 5(1), 1–10. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/148125
The intellectual property of articles belongs to the respective authors.
On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:
- Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.
- Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.
- Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.
- Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.
- The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.
- The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.