dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Heunen, Chris | |
dc.contributor.advisor | Oosten, Jaap van | |
dc.contributor.author | Hoorn, W.L.F. van der | |
dc.date.accessioned | 2011-11-09T18:00:43Z | |
dc.date.available | 2011-11-09 | |
dc.date.available | 2011-11-09T18:00:43Z | |
dc.date.issued | 2011 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/9413 | |
dc.description.abstract | The role the choices of orthogonal bases play in the structure of the category
Hilb, remains a problem in categorical quantum mechanics. In this thesis we
take a closer look at the finite dimensional Hilbert spaces. We will show that
there is a link between these and certain inverse semigroups. Thus reducing
this geometric problem to a problem in the field of combinatorics.
Using the work of Samson Abramsky et al., we will show that we have an
equivalence between the categories Frob(PInj) and Frob(Hilb) of Frobenius
semigroups. Next, we will study symmetric inverse semigroups and construct
the category RepInv of representable inverse semigroups. Using the above
equivalence and theWagner-Preston representation we prove that we have an
adjunction between RepInv and Frob(Hilb). This shows that these inverse
semigroups carry a structure similar to that of finite- dimensional Hilbert
spaces. | |
dc.description.sponsorship | Utrecht University | |
dc.format.extent | 601574 bytes | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Orthonormal bases in Inverse semigroups, a
categorical approach | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.courseuu | Mathematical Sciences | |