FROBENIJUSOVE ALGEBRE I TOPOLOŠKE KVANTNE TEORIJE POLJA

eBiblioteka

 
 

FROBENIJUSOVE ALGEBRE I TOPOLOŠKE KVANTNE TEORIJE POLJA

Show simple item record

dc.contributor.advisor Petrić, Zoran
dc.contributor.author Telebaković Onić, Sonja
dc.date.accessioned 2022-04-13T13:39:33Z
dc.date.available 2022-04-13T13:39:33Z
dc.date.issued 2022-04
dc.identifier.uri http://hdl.handle.net/123456789/5353
dc.description.abstract n this dissertation the connection between Frobenius algebras and topological quantum field theories (TQFTs) is investigated. It is well-known that each 2-dimensional TQFT (2-TQFT) corresponds to a commutative Frobenius algebra and conversely, i.e., that the category whose objects are 2-TQFTs is equivalent to the category of commutative Frobe- nius algebras. Every 2-TQFT is completely determined by the image of 1-dimensional sphere S1 and by its values on the generators of the category of 2-dimensional oriented cobordisms. Relations that hold for these cobordisms correspond precisely to the axioms of a commutative Frobenius algebra. Following the pattern of the Frobenius structure assigned to the sphere S1 in this way, we examine the Frobenius structure of spheres in all other dimensions. For every d ≥ 2, the sphere Sd−1 is a commutative Frobenius object in the category of d-dimensional cobordisms. We prove that there is no distinction between spheres Sd−1, for d ≥ 2, because they are all free of additional equations formulated in the language of multiplication, unit, comultiplication and counit. The only exception is the sphere S0 which is a symmetric Frobenius object but not commutative. The sphere S0 is mapped to a matrix Frobenius algebra by the Brauerian representation, which is an example of a faithful 1-TQFT functor. We obtain the faithfulness result for all 1-TQFTs, mapping the 0-dimensional manifold, consisting of one point to a vector space of dimension at least 2. Finally, we show that the commutative Frobenius algebra QZ5 ⊗ Z(QS3), defined as the ten- sor product of the group algebra and the centre of the group algebra, corresponds to the faithful 2-TQFT. It means that 2-dimensional cobordisms are equivalent if and only if the corresponding linear maps are equal. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2022-04-13T13:39:33Z No. of bitstreams: 1 stoDisertacijaOnic.pdf: 9095116 bytes, checksum: c0de7582fa89b5447c852701f7b45dca (MD5) en
dc.description.provenance Made available in DSpace on 2022-04-13T13:39:33Z (GMT). No. of bitstreams: 1 stoDisertacijaOnic.pdf: 9095116 bytes, checksum: c0de7582fa89b5447c852701f7b45dca (MD5) Previous issue date: 2022-04 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title FROBENIJUSOVE ALGEBRE I TOPOLOŠKE KVANTNE TEORIJE POLJA en_US
mf.author.birth-date 1981-08-20
mf.author.birth-place Beograd en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Frobenius algebra, topological quantum field theory, symmetric Frobenius ob- ject, faithful functor, oriented manifold, cobordism, normal form, Brauerian representation, Kronecker product, commutation matrix, Zsigmondy’s Theorem en_US
mf.subject.subarea Algebra en_US
mf.contributor.committee Živaljević, Rade
mf.contributor.committee Lipkovski, Aleksandar
mf.contributor.committee Radovanović, Marko
mf.contributor.committee Baralić, Đorđe
mf.university.faculty Mathematical faculty en_US
mf.document.references 48 en_US
mf.document.pages 89 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

Files in this item

Files Size Format View
stoDisertacijaOnic.pdf 9.095Mb PDF View/Open

This item appears in the following Collection(s)

Show simple item record