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Oxford Quantum Talks Archive

Advanced graphical calculus - Hopf, Frobenius, Schur and some motivation from group theory

Bertfried Fauser, University of Birmingham
Categories, Logic and Foundations of Physics VI, March 2010, University of Oxford

Graphical calculus has become a tool in quantum information theory, especially the Frobenius algebra structure for modelling the copying of classical information and rewriting rules. In my talk I will try to provide a more general picture including a Hopf algebra structure, Hopf algebra cohomology and the operation of composition. The underlying isoclasses of vector spaces will be countably infinite. The development will be motivated by findings in group theory, particularly the theory of group chraraters, which will serve as running example. If time permits I will also address conformal fields.

[slides]