120 research outputs found
Logarithmic intertwining operators and W(2,2p-1)-algebras
For every , we obtained an explicit construction of a family of
-modules, which decompose as direct sum of simple Virasoro
algebra modules. Furthermore, we classified all irreducible self-dual
-modules, we described their internal structure, and
computed their graded dimensions. In addition, we constructed certain hidden
logarithmic intertwining operators among two ordinary and one logarithmic
-modules. This work, in particular, gives a mathematically
precise formulation and interpretation of what physicists have been referring
to as "logarithmic conformal field theory" of central charge
. Our explicit construction can be
easily applied for computations of correlation functions. Techniques from this
paper can be used to study the triplet vertex operator algebra
and other logarithmic models.Comment: 22 pages; v2: misprints corrected, other minor changes. Final version
to appear in Journal of Math. Phy
An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}
By extending the methods used in our earlier work, in this paper, we present
an explicit realization of logarithmic \mathcal{W}_{p,p'}-modules that have
L(0) nilpotent rank three. This was achieved by combining the techniques
developed in \cite{AdM-2009} with the theory of local systems of vertex
operators \cite{LL}. In addition, we also construct a new type of extension of
, denoted by . Our results confirm several
claims in the physics literature regarding the structure of projective covers
of certain irreducible representations in the principal block. This approach
can be applied to other models defined via a pair screenings.Comment: 18 pages, v2: one reference added, other minor change
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
Representations of vertex algebras
In this paper we present some results on the representation theory of
vertex operator (super) algebras associated to affine Lie algebras and
Neveu-Schwarz algebra
The N=1 triplet vertex operator superalgebras
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras
SW(m), , which are natural super analogs of the triplet vertex
algebra family W(p), , important in logarithmic conformal field
theory. We classify irreducible SW(m)-modules and discuss logarithmic modules.
We also compute bosonic and fermionic formulas of irreducible SW(m) characters.
Finally, we contemplate possible connections between the category of
SW(m)-modules and the category of modules for the quantum group
U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on
properties of characters and the Zhu's algebra A(SW(m)). This paper is a
continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version,
to appear in CM
Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level
We introduce the infinite-dimensional Lie superalgebra and
construct a family of mappings from certain category of -modules
to the category of A_1^(1)-modules of critical level. Using this approach, we
prove the irreducibility of a family of A_1^(1)-modules at the critical level.
As a consequence, we present a new proof of irreducibility of certain
Wakimoto modules. We also give a natural realizations of irreducible quotients
of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late
On Free Field Realizations of W(2,2)-Modules
The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra H at level zero as modules for the W(2,2)-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322-4342, arXiv:1405.1707]. We prove that the irreducible highest weight H-module is irreducible as W(2,2)-module if and only if it has a typical highest weight. Finally, we construct a screening operator acting on the Heisenberg-Virasoro vertex algebra whose kernel is exactly W(2,2) vertex algebra
Wear Behaviour of Hard Cr Coatings for Cold Forming Tools Under Dry Sliding Conditions
Cr hard coatings are largely used in industry in metal cutting and cold forming processes; This work on quantitative way represents improvement, in terms of wear resistance, which is obtained by depositing Cr hard coating on foundation material. Wear testing is done on tribometer with block –on –disc contact geometry at sliding contact of Cr hard coated sample with steel disc. Testing was performed in conditions without lubrication at variable value of contact parameters (normal load, sliding speed). Cr hard coatings in all contact conditions show smaller values of wear rate
Morfometrijske i mehaničke osobine kostiju nogu kod pilića autohtonih rasa gološijana u Srbiji
The purpose of this study was to estimate the morphometric and mechanical parameters of femur and tibiotarsal bone in male and female chickens of three Serbian autochthonous naked neck breeds (white, black and gray) and compared these values with chickens of commercial naked neck hybrid Farm Q. Chickens were reared in extensive system and fattening lasted 98 days (14 weeks) The bone length, weight, cross sectional diaphyseal geometry (total area, medullar area, cortical area) and bone breaking force were determined. Between the varieties of autochthonous naked neck breeds, the presence of significant difference was not established. Average bone mass and length, of femur in male chickens were 13.6 g and 8.2 cm and for tibiotarsal bone, 19.5 g and 11.7 cm. In a female chickens those values were 10.6 g and 7.8 cm for femur and 15.9 g and 11.0 cm for tibiotarsus. In a male chickens average breaking force of femur (36.1 kg) and tibiotarsus (31.6 kg) were higher than those in a female chickens (27.0; 29.6 kg, respectively). In comparison with chickens of commercial naked neck hybrid (Farm Q), chickens of three Serbian autochthonous naked neck breeds have had significantly lower (P (lt) 0.05) bone mass, cross sectional diaphyseal area and cross sectional medullar area. Bone length and cross sectional cortical area were not significantly differed. However, tibiotarsal strength, expressed as bone breaking force, were signifficantly (P (lt) 0.05) higher in a chickens of autochthonous naked neck breeds.Cilj ispitivanja je bio da se ustanove morfometrijske i mehaničke osobine kostiju nogu (butna kost i golenjača) pilića tri autohtona varijeteta gološijana koji se gaje u Srbiji (beli, crni i sivi) i poređenje tih rezultata sa parametrima golenjače komercijalnog hibrida gološijana Farm Q. Pilići su gajeni u ekstenzivnim uslovima a period tova je trajao 98 dana (14 nedelja). Na desnoj butnoj kosti i golenjači određivani su masa, dužina, parametri geometrije preseka dijafize (površina preseka dijafize, površina preseka medularne šupljine i površina preseka korteksa) i sila loma. Između varijeteta autohtonih pilića gološijana nije ustanovljeno postojanje značajnih razlika u osobinama kostiju ali su muški pilići ispoljili veće vrednosti u odnosu na ženke. Prosečne vrednosti mase i dužine butne kosti, kod muških pilića su iznosile 13.6 g i 8.2 cm a golenjače 19.5 g i 11.7 cm. Kod ženki ove vrednosti su prosečno iznosile, za butnu kost 10.6 g i 7.8 cm a za golenjaču 15.9 g i 11.0 cm. Vrednosti sile loma ispitivanih kostiju su pokazale da autohtoni gološijani imaju dobru čvrstoću kostiju. Kod mužjaka, prosečna sila loma butne kosti (36.1 kg) i golenjače (31.6 kg) su bile veće nego kod ženki (20.0 kg - butna kost; 29.6 kg - golenjača). U poređenju sa pilićima komercijalnog hibrida glošijana Farm Q, pilići autohtonih varijeteta su imali značajno (p (lt) 0.05) manju masu golenjače, površinu preseka dijafize i medularne šupljine. Dužina kosti i površina preseka korteksa se nisu značajno razlikovale. Međutim, čvrstoća golenjače, izražena kroz silu loma, bila je značajno (P (lt) 0.05) veća kod pilića autohtonih varijeteta gološijana
Early potato
The harvest area of potatoes in South East Europe is about 580 000 ha with a production of about 11 000 000 tonnes. It is estimated that 20–25% of all harvested area is used for early potatoes. Early potato is of high biological and nutritional value, and is suitable for growing on small family-run commercial farms. In the continental area of South and South East Europe, new potato matures for harvest in late May, June and early July. In recent years, early potato has reached the market 20–25 days earlier thanks to the adoption of specific cultivation practices and growing technologies, as well as an increase in financial input per unit area. As the first spring vegetable, early potato is considered a supreme biological and economic crop. The first precondition for high, stable and quality production of early potato is the choice of very early-maturing cultivars with high yield potential, good adaptability and stability. The second precondition is the planting of equally sprouted and certified seedlings with mulching and crop covering with agrotextiles. In the continental area of South and South East Europe, apart from early potato farming in temporary protected areas – for example, direct crop covering with or without mulching and in low plastic tunnels – early potato is also grown in large plastic tunnels without additional heating. Early potato is planted in mid-February in the Mediterranean area. This is 30 days earlier than in the continental area, and when covered with agrotextiles it can be harvested even earlier. This chapter presents some biological and agrotechnological aspects, such as biological needs, fertilization, irrigation, harvesting and storage of early potatoes
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