Abstract
Commutative Frobenius algebras play an important role in both TQFT and CQM; in the first case they correspond to 2d TQFTs, while in the second they are non-degenerate observables. I will consider the case of “special” Frobenius algebras, and their associated group of phases. This gives rise to a free construction from the category of abelian groups to the PROP generated by this Frobenius algebra. Of course a theory with only one observable is not very interesting. I will consider how two such PROPs should be combined, and show that if the two algebras (i) jointly form a bialgebra and (ii) their units are “mutually real”; then they jointly form a Hopf algebra. This gives a free model of a pair of strongly complementary observables. I will also consider which unitary maps must exist in such models.
| Original language | English |
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| Publication status | Published - 2015 |
| Event | Higher TQFT and categorical quantum mechanics - Erwin Schrödinger Institute, Vienna, Austria Duration: 19 Oct 2015 → 23 Oct 2015 http://www.esi.ac.at/activities/events/2015/higher-topological-quantum-field-theory-and-categorical-quantum-mechanics |
Workshop
| Workshop | Higher TQFT and categorical quantum mechanics |
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| Country/Territory | Austria |
| City | Vienna |
| Period | 19/10/15 → 23/10/15 |
| Internet address |
Keywords
- higher topological quantum field theory
- e Frobenius algebras
- categorical quantum mechanics
- abelian groups
- Hopf algebra
- bialgebra