University of Oxford Logo University of OxfordDepartment of Computer Science - Home
On Facebook
Facebook
Follow us on twitter
Twitter
Linked in
Linked in
Flickr
Flickr
Google plus
Google plus
Digg
Digg
Pinterest
Pinterest
Stumble Upon
Stumble Upon

Oxford Quantum Talks Archive

Some graphical aspects of Frobenius algebra

Bertfried Fauser, University of Birmingham
Flowin'Cat 2010, October 2010, University of Oxford

There exists a vast literature on Frobenius extensions and Frobenius structures, and this is still a very active field of research. Frobenius structures may by studied in a combinatorial, algebraic geometric or categorical fashion. In this talk we use graphical calculus of isotopy classes of tangles to study some aspects of Frobenius structures. I will especially review the topological move, `yanking up-down-bends straight', used in the qBit case to model the quantum information flow in, for example, the teleportation protocol. It will be shown how to generalize this in an infinite dimensional setting using a deformation on the characters of such representations. If time permits, we will encounter braid and Yang-Baxter relations, and hence have to move from symmetric to braided monoidal structures.

[video] [streaming video] [slides]