Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-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

Quantum-sl(2) action on a divided-power quantum plane at even roots of unity

We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$ by nilpotents. For this quantum plane, we construct a Wess--Zumino-type de Rham complex and find its decomposition into representations of the $2p^3$-dimensional quantum group $U_q sl(2)$ and its Lusztig extension; the quantum group action is also defined on the algebra of quantum differential operators on the quantum plane.Comment: 18 pages, amsart++, xy, times. V2: a reference and related comments adde

Generalized twisted modules associated to general automorphisms of a vertex operator algebra

We introduce a notion of strongly C^{\times}-graded, or equivalently, C/Z-graded generalized g-twisted V-module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V-module if V admits an additional C-grading compatible with g. Let V=\coprod_{n\in \Z}V_{(n)} be a vertex operator algebra such that V_{(0)}=\C\one and V_{(n)}=0 for n<0 and let u be an element of V of weight 1 such that L(1)u=0. Then the exponential of 2\pi \sqrt{-1} Res_{x} Y(u, x) is an automorphism g_{u} of V. In this case, a strongly C-graded generalized g_{u}-twisted V-module is constructed from a strongly C-graded generalized V-module with a compatible action of g_{u} by modifying the vertex operator map for the generalized V-module using the exponential of the negative-power part of the vertex operator Y(u, x). In particular, we give examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet W-algebras. An important feature is that we have to work with generalized (twisted) V-modules which are doubly graded by the group C/Z or C and by generalized eigenspaces (not just eigenspaces) for L(0), and the twisted vertex operators in general involve the logarithm of the formal variable.Comment: Final version to appear in Comm. Math. Phys. 38 pages. References on triplet W-algebras added, misprints corrected, and expositions revise

Impregnation of cellulose acetate films with carvacrol using supercritical carbon ioxide

Cellulose acetate films were impregnated with carvacrol using supercritical carbon dioxide. The supercritical impregnation process, conducted in a static regime at pressure of 21 MPa and temperature of 50°C, was optimized by variation in the processing time (30 and 120 min) and decompression rate (from 0.3 MPa/min to 36 MPa/min). Characterization of the obtained cellulose acetate films was performed by Atomic Force Microscopy and Differential Scanning Calorimetry. Effects of glycerol and carvacrol on the properties of the films were discussed. Release kinetics from the cellulose acetate film with 31.4% of carvacrol was investigated in a physiological saline solution. In addition, the Higuchi and Korsmeyer-Peppas release models fitted the carvacrol release curve well. Obtained cellulose acetate films impregnated with carvacrol can be of interest for the application in medicine as wound dressings considering their biocompatibility and biodegradability as well as their potential antimicrobial activity or in the food industry as an active food packaging

Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra

We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in the (p,1) logarithmic models of conformal field theory. For this, the category of Yetter-Drinfeld modules is to be regarded as an \textit{entwined} category (the one with monodromy, but not with braiding).Comment: 36 pages, amsart++, times, xy. V3: references added, an unnecessary assumption removed, plus some minor change

A differential U-module algebra for U=U_q sl(2) at an even root of unity

We show that the full matrix algebra Mat_p(C) is a U-module algebra for U = U_q sl(2), a 2p^3-dimensional quantum sl(2) group at the 2p-th root of unity. Mat_p(C) decomposes into a direct sum of projective U-modules P^+_n with all odd n, 1<=n<=p. In terms of generators and relations, this U-module algebra is described as the algebra of q-differential operators "in one variable" with the relations D z = q - q^{-1} + q^{-2} z D and z^p = D^p = 0. These relations define a "parafermionic" statistics that generalizes the fermionic commutation relations. By the Kazhdan--Lusztig duality, it is to be realized in a manifestly quantum-group-symmetric description of (p,1) logarithmic conformal field models. We extend the Kazhdan--Lusztig duality between U and the (p,1) logarithmic models by constructing a quantum de Rham complex of the new U-module algebra.Comment: 29 pages, amsart++, xypics. V3: The differential U-module algebra was claimed quantum commutative erroneously. This is now corrected, the other results unaffecte

Logarithmic and complex constant term identities

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamovic and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove complex and logarithmic constant term identities for the root system G_2.Comment: 26 page

W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)

We construct new Yang-Baxter integrable boundary conditions in the lattice approach to the logarithmic minimal model WLM(1,p) giving rise to reducible yet indecomposable representations of rank 1 in the continuum scaling limit. We interpret these W-extended Kac representations as finitely-generated W-extended Feigin-Fuchs modules over the triplet W-algebra W(p). The W-extended fusion rules of these representations are inferred from the recently conjectured Virasoro fusion rules of the Kac representations in the underlying logarithmic minimal model LM(1,p). We also introduce the modules contragredient to the W-extended Kac modules and work out the correspondingly-extended fusion algebra. Our results are in accordance with the Kazhdan-Lusztig dual of tensor products of modules over the restricted quantum universal enveloping algebra $\bar{U}_q(sl_2)$ at $q=e^{\pi i/p}$. Finally, polynomial fusion rings isomorphic with the various fusion algebras are determined, and the corresponding Grothendieck ring of characters is identified.Comment: 28 page

Degradation of aflatoxin B1 from naturally contaminated maize using the edible fungus Pleurotus ostreatus

Aflatoxins are highly carcinogenic secondary metabolites that can contaminate approximately 25% of crops and that cause or exacerbate multiple adverse health conditions, especially in Sub-Saharan Africa and South and Southeast Asia. Regulation and decontamination of aflatoxins in high exposure areas is lacking. Biological detoxification methods are promising because they are assumed to be cheaper and more environmentally friendly compared to chemical alternatives. White-rot fungi produce non-specific enzymes that are known to degrade aflatoxin in in situ and ex situ experiments. The aims of this study were to (1) decontaminate aflatoxin-B-1-(AFB(1)) in naturally contaminated maize with the edible, white-rot fungus Pleurotus ostreatus (oyster mushroom) using a solid-state fermentation system that followed standard cultivation techniques, and to (2) and to assess the risk of mutagenicity in the resulting breakdown products and mushrooms. Vegetative growth and yield characteristics of P. ostreatus were not inhibited by the presence of-AFB(1).-AFB(1) was degraded by up to 94% by the Blue strain. No aflatoxin could be detected in P. ostreatus mushrooms produced from-AFB(1)-contaminated maize. Moreover, the mutagenicity of breakdown products from the maize substrate, and reversion of breakdown products to the parent compound, were minimal. These results suggest that P. ostreatus significantly degrades-AFB(1) in naturally contaminated maize under standard cultivation techniques to levels that are acceptable for some livestock fodder, and that using P. ostreatus to bioconvert crops into mushrooms can reduce-AFB(1)-related losses.University of Arizona Green Fund [GF 15.31]Open Access Journal.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Shift of the western boundary of the distribution area of Micromeria cristata (Hampe) Griseb. and Steptorhamphus tuberosus (Jacq.) Grossh.

During field investigations of Mt Rumija, two new taxa for the flora of Montenegro were recorded: Micromeria cristata (Hampe) Griseb. and Steptorhamphus tuberosus (Jacq.) Grossh. From the phytogeographic point of view these data indicate a change in the distribution area of both taxa, which have shifted to the west. Ashort overview of the taxonomic treatment of both genera is given