Jump to ContentJump to Main Navigation
Quantum Physics and LinguisticsA Compositional, Diagrammatic Discourse$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 08 April 2020

Some Graphical Aspects of Frobenius Algebras

Some Graphical Aspects of Frobenius Algebras

Chapter:
(p.22) CHAPTER 2 Some Graphical Aspects of Frobenius Algebras
Source:
Quantum Physics and Linguistics
Author(s):

Fauser Bertfried

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199646296.003.0002

Frobenius algebras surface at many places in mathematics and physics. Quite recently, using a convenient graphical notation, Frobenius algebras have been used to investigate foundational issues of quantum theory— references will be given below. Also, as shown elsewhere in this book, Frobenius algebras emerge in the semantic analysis of natural languages. The aim of this chapter is to present the basic results of Frobenius algebras and their relation to finite-dimensional Hopf algebras, with special emphasis on use of graphical notation. Frobenius structures, which are related to ring theory, need to be considered too. Frobenius structures encode such notions as semi-simplicity and separability of rings. We occasionally need to extend the graphical calculus to encode properties of underlying rings, but will not venture properly into 2-categorical notions. Moreover, no new results may be found in this chapter, and far from everything that is known about the subject is covered here. However, in passing we will give some pointers to the literature, which unfortunately is far too large to be considered completely.

Keywords:   frobenius algebras, graphical notation, hopf algebras, rings, quantum groups

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .