Title Verteks algebre pridružene reprezentacijama N=1 super Heisenberg-Virasorove i Schrödinger-Virasorove algebre Title (english) Vertex algebras associated with the representations of the N=1 super Heisenberg-Virasoro and Schrödinger-Virasoro algebras Author Berislav Jandrić Mentor Dražen Adamović (mentor)Committee member Gordan Radobolja (predsjednik povjerenstva)Committee member Dražen Adamović (član povjerenstva)Committee member Ozren Perše (član povjerenstva)Granter University of Zagreb Defense date and country 2019-07-08, Croatia Scientific / art field, NATURAL SCIENCES Universal decimal classificationUDC ) 51 - Mathematics Abstract U ovom radu proučavali smo teoriju reprezentacija dviju važnih generalizacija Heisenberg-Virasorove Liejeve algebre
H , a to su N = 1 super Heisenberg-Virasorova Liejeva algebra
S H i Schrödinger-Virasorova Liejeva algebra
s v . Prva predstavlja primjer beskonačnodimenzionalne Liejeve super-algebre koja do sada nije bila otkrivena, dok je druga primjer beskonačno dimenzionalne Liejeve algebre koja se dosta proučavala u fizikalnoj kao i matematičkoj
... More literaturi jer je prva u seriji tzv. galilejevskih Liejevih konformnih algebri proširenih tzv. nerelativističkim spinom. Originalan doprinos ovog rada je eksplicitna konstrukcija izomorfizma univerzalne (resp. proste) omotačke verteks super-algebre V S H ( c L , c L , α , c α ≠ 0 ) L S H ( c L , c L , α , c α ≠ 0 ) S H S M ( 1 ) ⨂ V N S c L − c μ S M ( 1 ) ⨂ L N S c L − c μ S M ( 1 ) L S H ( 3 2 − 3 μ 2 , μ 2 c α , c α ) , c α ≠ 0 V S H ( c L , c L , α , c α ≠ 0 ) c α = 0 H 1 2 , 1 , 3 2 , 2 S H p 2 p s v V s v ( c L , c L , β , c β ) Less Abstract (english) In this thesis we have investigated representation theory of two important generalizations of the Hesienberg-Virasoro Lie algebra
H , which are the N = 1 super Heisenberg-Virasoro Lie algebra
S H and the Schrödinger-Virasoro Lie algebra
s v . The former provides an example of an infinite dimensional Lie super-algebra which has not been yet discovered, while the latter is also an example of an infinite dimensional Lie algebra that has been widely
... More studied in the physical as well as mathematical literature because it is the first of an infinite series of the so called Galilean Lie conformal algebras extended by the non-relativistic spin parametre. The important innovation in this thesis is the explicit construction of an isomorphism between the universal (resp. simple) enveloping vertex superalgebra V S H ( c L , c L , α , c α ≠ 0 ) L S H ( c L , c L , α , c α ≠ 0 ) S H S M ( 1 ) ⨂ V N S c L − c μ S M ( 1 ) ⨂ L N S c L − c μ L S H ( 3 2 − 3 μ 2 , μ 2 c α , c α ) , c α ≠ 0 S M ( 1 ) c α = 0 1 2 , 1 , 3 2 , 2 S H p 2 p s v V s v ( c L , c L , β , c β ) Less Keywords
verteks-algebra
N=1 Heisenberg-Virasorova verteksalgebra
N=1 Neveu-Schwarz Liejeva algebra
singularni vektori
screening operatori
Schrödinger-Virasorova verteks-algebra
Keywords (english)
vertex algebra
N=1 Heisenberg-Virasoro vertex algebra
N=1 Neveu-Schwarz Lie algebra
singular vector
screening operator
SchrödingerVirasoro vertex algebra
Language croatian URN:NBN urn:nbn:hr:217:925217 Study programme Title: Mathematics Type of resource Text Extent vii, 88 str. File origin Born digital Access conditions Open access Terms of use Created on 2019-07-16 11:08:28
