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## Hopf Algebras—Variant Notions and Reconstruction Theorems

*Joost Vercruysse*

### in Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199646296
- eISBN:
- 9780191747847
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646296.003.0005
- Subject:
- Mathematics, Applied Mathematics

Hopf algebras are closely related to monoidal categories. More precisely, k-Hopf algebras can be characterized as those algebras whose category of finite-dimensional representations is an autonomous ... More

## Epilogue: Miscellaneous Topics and Possible Extensions

*Gerald W. Johnson, Michel L. Lapidus, and Lance Nielsen*

### in Feynman's Operational Calculus and Beyond: Noncommutativity and Time-Ordering

- Published in print:
- 2015
- Published Online:
- September 2015
- ISBN:
- 9780198702498
- eISBN:
- 9780191772160
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198702498.003.0011
- Subject:
- Mathematics, Mathematical Physics, Numerical Analysis

A brief discussion is given of possible extensions to the theory developed in this book, and suggestions for the direction of future research in this general area are given. This is done via a ... More

## Complementarity

*Chris Heunen and Jamie Vicary*

### in Categories for Quantum Theory: An Introduction

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780198739623
- eISBN:
- 9780191802584
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198739623.003.0006
- Subject:
- Mathematics, Mathematical Physics, Applied Mathematics

Complementarity is a property of a pair of observables being ‘maximally distinct’ from each other and, in this chapter, we analyse this property in categorical terms as a pair of interacting ... More

## Categories for Quantum Theory: An Introduction

*Chris Heunen and Jamie Vicary*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780198739623
- eISBN:
- 9780191802584
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198739623.001.0001
- Subject:
- Mathematics, Mathematical Physics, Applied Mathematics

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to ... More

## The Secondary Characteristic Classes

*Ercüment H. Ortaçgil*

### in An Alternative Approach to Lie Groups and Geometric Structures

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198821656
- eISBN:
- 9780191860959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821656.003.0013
- Subject:
- Mathematics, Pure Mathematics

Changing the representation bundle from T to T ⊗ T∗ gives a sequence where both torsion and curvature live. Vanishing of the curvature gives rise to some closed forms.

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