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Quantum Physics and LinguisticsA Compositional, Diagrammatic Discourse$
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Chris Heunen, Mehrnoosh Sadrzadeh, and Edward Grefenstette

Print publication date: 2013

Print ISBN-13: 9780199646296

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199646296.001.0001

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Quantum Groups and Braided Algebra

Quantum Groups and Braided Algebra

Chapter:
(p.90) CHAPTER 4 Quantum Groups and Braided Algebra
Source:
Quantum Physics and Linguistics
Author(s):

Shahn Majid

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199646296.003.0004

We describe a way of doing group theory or quantum group theory, developed in the 1990s in which algebra is ‘wired up’ in much the same way as a computer except that there is a non-trivial braid operator when two wires cross. Such braided flow charts may be the relevant syntax for certain types of quantum computer and are part of the intrinsic geometry of all quasitriangular quantum groups including their associated braided-Lie algebras. We also look at geometry in monoidal catgories.

Keywords:   quantum groups, wire diagrams, braided Lie algebras, monoidal categories

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