22 research outputs found
On coset vertex algebras with central charge 1
We present a coset realization of the vertex operator algebra with central charge .
We investigate the vertex operator algebra (resp. ) as a vertex
subalgebra of (resp. ). Our construction is based on the
boson-fermion correspondence and certain conformal embeddings
Conformal embeddings in affine vertex superalgebras
This paper is a natural continuation of our previous work on conformal
embeddings of vertex algebras [6], [7], [8]. Here we consider conformal
embeddings in simple affine vertex superalgebra where
is a basic
classical simple Lie superalgebras. Let
be the subalgebra of generated by . We
first classify all levels for which the embedding in is conformal. Next we prove that, for a
large family of such conformal levels, is a completely
reducible --module and obtain
decomposition rules. Proofs are based on fusion rules arguments and on the
representation theory of certain affine vertex algebras. The most interesting
case is the decomposition of as a finite, non
simple current extension of . This
decomposition uses our previous work [10] on the representation theory of
.Comment: Latex file, 45 pages, to appear in Advances in Mathematic
Cross product on (mathbb{R}^{n}), normed algebras and H–spaces
U ovom preglednom radu prezentiramo konstrukciju vektorskog produkta na (mathbb{R}^{n}), danu u radu P. F. McLoughlin, arXiv:1212.3515. Pokazujemo da vektorski produkt, definiran na prirodan način, postoji samo za n = 0, 1, 3, 7 (pritom s (mathbb{R}^{0}) označavamo nulprostor nad (mathbb{R}) ). Proučavamo vezu vektorskog produkta s Hurwitzovim teoremom o postojanju normiranih algebri samo za dimenzije n = 1, 2, 4, 8, te s Adamsovim teoremom o neprekidnim množenjima na sferi. Također, proučavamo mogućnosti generalizacije vektorskog produkta na ( mathbb{R}^{n}) , s funkcije dvije varijable na funkciju više varijabli.In this survey article, we present a construction of the cross product on (mathbb{R}^{n}) , following the paper by P. F. McLoughlin, arXiv:1212.3515. We show that a naturally defined cross product exists only for n = 0, 1, 3, 7 (here (mathbb{R}^{0}) denotes the zero vector space over (mathbb{R}) ). We study the relationship between the cross product and Hurwitz’s theorem on the existence of normed algebras only for dimensions n = 1, 2, 4, 8, and the relationship with Adams’ theorem on continuous multiplications on spheres. Furthermore, we consider the possibilities of a generalization of the cross product on (mathbb{R}^{0}) , from the function of two variables to the function of several variables
Alternativna definicija limesa funkcije
Autori prezentiraju jednu alternativnu definiciju limesa
Riemannova, Darbouxova i Cauchyjeva integrabilnost
U ovom preglednom radu prezentiramo dokaz iz S. Schneider, International Mathematical Forum 9 (2014) da se Riemannova i Cauchyjeva definicija integrabilnosti podudaraju. Također, diskutiramo odnos Riemannove i Darbouxove integrabilnosti
Representations of certain non-rational vertex operator algebras of affine type
In this paper we study a series of vertex operator algebras of integer level
associated to the affine Lie algebra . These vertex operator
algebras are constructed by using the explicit construction of certain singular
vectors in the universal affine vertex operator algebra at the
integer level. In the case or , we explicitly determine Zhu's
algebras and classify all irreducible modules in the category . In
the case , we show that the vertex operator algebra contains
two linearly independent singular vectors of the same conformal weight.Comment: 15 pages, LaTeX; final version, to appear in J. Algebr
Riemannova, Darbouxova i Cauchyjeva integrabilnost
U ovom preglednom radu prezentiramo dokaz iz S. Schneider, International Mathematical Forum 9 (2014) da se Riemannova i Cauchyjeva definicija integrabilnosti podudaraju. Također, diskutiramo odnos Riemannove i Darbouxove integrabilnosti
Fusion rules and complete reducibility of certain modules for affine Lie algebras
We develop a new method for obtaining branching rules for affine Kac-Moody
Lie algebras at negative integer levels. This method uses fusion rules for
vertex operator algebras of affine type. We prove that an infinite family of
ordinary modules for affine vertex algebra of type A investigated in Adamovi\'c
and O. Per\v{s}e (2008) is closed under fusion. Then we apply these fusion
rules on explicit bosonic realization of level -1 modules for the affine Lie
algebra of type , obtain a new proof of complete reducibility
for these representations, and the corresponding decomposition for . We also obtain the complete reducibility of the associated level -1 modules
for affine Lie algebra of type . Next we notice that the
category of modules at level obtained in
Per\v{s}e (2012) has the isomorphic fusion algebra. This enables us to
decompose certain and --modules at negative levels.Comment: 18 pages; final version, to appear in Journal of Algebra and Its
Application