Graph-algebras—faithful representations and mediating objects in mathematics

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Abstract

I consider the role of diagrams in contemporary mathematics. More specifically the role of certain diagrams—so-called directed graphs—will be investigated. I propose that these graphs act as mediating objects. This means that they link certain objects, that is, a C*-algebra and its associated K-groups, and that this link yields an epistemic gain. I explain that the link is possible because a graph represents as a metaphor in two distinct ways. In addition, the diagrammatic presentation of a directed graph becomes an object that can be manipulated. As such, it becomes what I will denote a “faithful representation.” The notion of a faithful representation tries to capture the fruitfulness of the combination of metaphorical representation with the possibility of controlled manipulation.
Original languageEnglish
JournalEndeavour
Volume42
Issue number2-3
Pages (from-to)180-188
ISSN0160-9327
DOIs
Publication statusPublished - 1. Jun 2018

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Keywords

  • Diagrams in contemporary mathematics
  • Faithful representations
  • Fruitfulness
  • Manipulations on signs
  • Mediating objects
  • Semiotics

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