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doctoral thesis
Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\)
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:209033
Polić, Marijan
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Polić, M. (2015). Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\) (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:209033

Polić, Marijan. "Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\)." Doctoral thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:209033

Polić, Marijan. "Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\)." Doctoral thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:209033

Polić, M. (2015). 'Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\)', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:209033

Polić M. Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\) [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:209033

M. Polić, "Reprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\)", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:209033

Metadata
TitleReprezentacije nekih podalgebri verteks algebre \(W_{1+\infty}\)
Title (english)Representations of certain subalgebras of the vertex algebra \(W_{1+\infty}\)
AuthorMarijan Polić
MentorDražen Adamović (mentor)
MentorOzren Perše (komentor)
Committee memberMirko Primc (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberOzren Perše (član povjerenstva)
Committee memberMiroslav Jerković (član povjerenstva)
Committee memberTomislav Šikić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-06-12, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
U radnji proučavamo strukturnu teoriju i teoriju reprezentacija verteks algebri \(W_{1+\infty}\) i \(W_\infty\) za neke centralne naboje. Dajemo eksplicitnu formulu za familiju singularnih vektora u univerzalnim verteks algebrama \(W_{1+\infty}\) i \(W_\infty\). Dokazano je da je netrivijalni kvocijent verteks algebre \(W_\infty\) za \(c =-2\) izomorfan \(W_{2,3}\) algebri iz članka W. Wanga [36]. U slučaju centralnog naboja \(c =-4\) prosti kvocijent od \(W_\infty\) je izomorfan parafermionskoj verteks algebri pridruženoj afinoj Liejevoj algebri \(A_1^{(1)}\) nivoa -1. U slučaju nekih drugih centralnih naboja određen je minimalan skup generatora kvocijenata univerzalne verteks–algebre za \(W_\infty\). Promatrana je teorija dualnih parova i realizirana je verteks algebra \(W_\infty\) kao podalgebra verteks superalgebre pridružene simplektičkim fermionima. Dokazano je da je verteks superalgebra pridružena simplektičkim fermionima potpuno reducibilna reprezentacija od \(W_\infty\).
Abstract (english)
In this thesis we study structure and representation theory for vertex algebras \(W_{1+\infty}\) and \(W_\infty\) for certain central charges. We give explicit formula for a family of singular vectors in universal vertex algebras \(W_{1+\infty}\) and \(W_\infty\) It is proved that a non-trivial quotient of the vertex algebra \(W_\infty\) with central charge \(c =-2\) is isomorphic to \(W_{2,3}\) algebra from the paper of W. Wang [36]. In the case of central charge \(c =-4\) simple quotient of \(W_\infty\) is isomorphic to the parafermionic vertex algebra associated to the affine Lie algebra \(A_1^{(1)}\) of the level -1. For some other central charges, the minimal set of generators for the quotient of universal vertex algebra of \(W_\infty\) is determined. The theory of dual pairs is used for realization of the vertex algebra \(W_\infty\) as a subalgebra of the vertex superalgebra associated to the symplectic fermions. It is proved that the vertex superalgebra associated to the symplectic fermions is completely reducible representation of \(W_\infty\).
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:209033
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentii, 80 str.
File originBorn digital
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Created on2019-03-21 10:56:39