The Diamond Lemma and the PBW Property in Quantum Algebras

(so3) is demonstrated. The approach presented here is successful in other cases of quantum algebras and superalgebras

Representations of the cyclically symmetric q-deformed algebra soq(3)so_q(3)

An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed. Not all irreducible representations of $U_q(sl_2)$ can be extended to representations of ${\hat U}_q(sl_2)$. Composing the homomorphism $\psi$ with irreducible representations of ${\hat U}_q(sl_2)$ we obtain representations of $U_q(so_3)$. Not all of these representations of $U_q(so_3)$ are irreducible. Reducible representations of $U_q(so_3)$ are decomposed into irreducible components. In this way we obtain all irreducible representations of $U_q(so_3)$ when $q$ is not a root of unity. A part of these representations turns into irreducible representations of the Lie algebra so$_3$ when $q\to 1$. Representations of the other part have no classical analogue. Using the homomorphism $\psi$ it is shown how to construct tensor products of finite dimensional representations of $U_q(so_3)$. Irreducible representations of $U_q(so_3)$ when $q$ is a root of unity are constructed. Part of them are obtained from irreducible representations of ${\hat U}_q(sl_2)$ by means of the homomorphism $\psi$.Comment: 28 pages, LaTe

Synthesis, X-ray structure determination and germination studies on some smoke-derived karrikins

AbstractThe discovery of the karrikin class of plant growth regulators (PGRs) is a milestone accomplishment in plant biochemistry and physiology, with significant potential in agriculture and horticulture. These compounds have in common a fused furano-pyran ring system featuring various permutations of methyl substitution. Chief amongst these compounds is karrikinolide (KAR1), identified as the key germination stimulant present in plant-derived smoke, which together with five other closely-related structures (KAR2–KAR6) make up the karrikin class of PGRs. By contrast, the germination inhibitor 3,4,5-trimethyl-2(5H)-furanone has also been identified in plant-derived smoke. Various synthetic endeavours have been undertaken for structure–activity relationship study purposes as well as to probe the molecular mechanics of these compounds. In this study, syntheses of KAR1, KAR3 and S-KAR1 were carried out and their structures verified by X-ray crystallography. Effects on germination were measured against the inhibitor 3,4,5-trimethyl-2(5H)-furanone in Grand Rapids lettuce seeds. X-ray crystallographic data and germination promotory activity for S-KAR1 are described for the first time

Three variable exponential functions of the alternating group

New class of special functions of three real variables, based on the alternating subgroup of the permutation group $S_3$, is studied. These functions are used for Fourier-like expansion of digital data given on lattice of any density and general position. Such functions have only trivial analogs in one and two variables; a connection to the $E-$functions of $C_3$ is shown. Continuous interpolation of the three dimensional data is studied and exemplified.Comment: 10 pages, 3 figure

Inocybe brijunica sp. nov., a new ectomycorrhizal fungus from Mediterranean Croatia revealed by morphology and multilocus phylogenetic analysis

A new ectomycorrhizal species was discovered during the first survey of fungal diversity at Brijuni National Park (Croatia), which consists of 14 islands and islets. The National Park is located in the Mediterranean Biogeographical Region, a prominent climate change hot-spot. Inocybe brijunica sp. nov., from sect. Hysterices (Agaricales, Inocybaceae), is described based on morphology and multilocus phylogenetic data. The holotype collection was found at the edge between grassland and Quercus ilex forest with a few planted Pinus pinea trees, on Veli Brijun Island, the largest island of the archipelago. It is easily recognized by a conspicuous orange to orange–red–brown membranaceous surface layer located at or just above the basal part of the stipe. Other distinctive features of I. brijunica are the medium brown, radially fibrillose to rimose pileus; pale to medium brown stipe with fugacious cortina; relatively small, amygdaliform to phaseoliform, and smooth basidiospores, measuring ca. 6.5–9 × 4–5.5 µm; thick-walled, utriform, lageniform or fusiform pleurocystidia (lamprocystidia) with crystals and mostly not yellowing in alkaline solutions; cheilocystidia of two types (lamprocystidia and leptocystidia); and the presence of abundant caulocystidia only in the upper 2–3 mm of the stipe. Phylogenetic reconstruction of a concatenated dataset of the internal transcribed spacer region (ITS), the nuclear 28S rRNA gene (nrLSU), and the second largest subunit of RNA polymerase II (rpb2) resolved I. brijunica and I. glabripes as sister species

Representations of the q-deformed algebra U'_q(so_4)

We study the nonstandard $q$-deformation $U'_q({\rm so}_4)$ of the universal enveloping algebra $U({\rm so}_4)$ obtained by deforming the defining relations for skew-symmetric generators of $U({\rm so}_4)$. This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism $\phi$ of $U'_q({\rm so}_4)$ to the certain nontrivial extension of the Drinfeld--Jimbo quantum algebra $U_q({\rm sl}_2)^{\otimes 2}$ and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finite dimensional representations of the classical type and of the nonclassical type for the algebra $U'_q({\rm so}_4)$. It is proved that for $q$ not a root of unity each irreducible finite dimensional representation of $U'_q({\rm so}_4)$ is equivalent to one of these representations. We prove that every finite dimensional representation of $U'_q({\rm so}_4)$ for $q$ not a root of unity is completely reducible. It is shown how to construct (by using the homomorphism $\phi$) tensor products of irreducible representations of $U'_q({\rm so}_4)$. (Note that no Hopf algebra structure is known for $U'_q({\rm so}_4)$.) These tensor products are decomposed into irreducible constituents.Comment: 28 pages, LaTe

A new approach to deformation equations of noncommutative KP hierarchies

Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly nonassociative' (WNA) algebra structure, from which we can conclude, refering to previous work, that any solution of the Riccati system also solves the potential KP hierarchy (in the corresponding matrix algebra). We then turn to the case where the components of the matrices are multiplied using a (generalized) star product. Associated with the deformation parameters, there are additional symmetries (flow equations) which enlarge the respective KP hierarchy. They have a compact formulation in terms of the WNA structure. We also present a formulation of the KP hierarchy equations themselves as deformation flow equations.Comment: 25 page

Fungal Planet description sheets: 1042–1111

Novel species of fungi described in this study include those from various countries as follows: Antarctica, Cladosporium arenosum from marine sediment sand. Argentina, Kosmimatamyces alatophylus (incl. Kosmimatamyces gen. nov.) from soil. Australia, Aspergillus banksianus, Aspergillus kumbius, Aspergillus luteorubrus, Aspergillus malvicolor and Aspergillus nanangensis from soil, Erysiphe medicaginis from leaves of Medicago polymorpha, Hymenotorrendiella communis on leaf litter of Eucalyptus bicostata, Lactifluus albopicri and Lactifluus austropiperatus on soil, Macalpinomyces collinsiae on Eriachne benthamii, Marasmius vagus on soil, Microdochium dawsoniorum from leaves of Sporobolus natalensis, Neopestalotiopsis nebuloides from leaves of Sporobolus elongatus, Pestalotiopsis etonensis from leaves of Sporobolus jacquemontii, Phytophthora personensis from soil associated with dying Grevillea mccutcheonii. Brazil, Aspergillus oxumiae from soil, Calvatia baixaverdensis on soil, Geastrum calycicoriaceum on leaf litter, Greeneria kielmeyerae on leaf spots of Kielmeyera coriacea. Chile, Phytophthora aysenensis on collar rot and stem of Aristotelia chilensis. Croatia, Mollisia gibbospora on fallen branch of Fagus sylvatica. Czech Republic, Neosetophoma hnaniceana from Buxus sempervirens. Ecuador, Exophiala frigidotolerans from soil. Estonia, Elaphomyces bucholtzii in soil. France, Venturia paralias from leaves of Euphorbia paralias. India, Cortinarius balteatoindicus and Cortinarius ulkhagarhiensis on leaf litter. Indonesia, Hymenotorrendiella indonesiana on Eucalyptus urophylla leaf litter. Italy, Penicillium taurinense from indoor chestnut mill. Malaysia, Hemileucoglossum kelabitense on soil, Satchmopsis pini on dead needles of Pinus tecunumanii. Poland, Lecanicillium praecognitum on insects' frass. Portugal, Neodevriesia aestuarina from saline water. Republic of Korea, Gongronella namwonensis from freshwater. Russia, Candida pellucida from Exomias pellucidus, Heterocephalacria septentrionalis as endophyte from Cladonia rangiferina, Vishniacozyma phoenicis from dates fruit, Volvariella paludosa from swamp. Slovenia, Mallocybe crassivelata on soil. South Africa, Beltraniella podocarpi, Hamatocanthoscypha podocarpi, Coleophoma podocarpi and Nothoseiridium podocarpi (incl. Nothoseiridium gen. nov.)from leaves of Podocarpus latifolius, Gyrothrix encephalarti from leaves of Encephalartos sp., Paraphyton cutaneum from skin of human patient, Phacidiella alsophilae from leaves of Alsophila capensis, and Satchmopsis metrosideri on leaf litter of Metrosideros excelsa. Spain, Cladophialophora cabanerensis from soil, Cortinarius paezii on soil, Cylindrium magnoliae from leaves of Magnolia grandiflora, Trichophoma cylindrospora (incl. Trichophoma gen. nov.) from plant debris, Tuber alcaracense in calcareus soil, Tuber buendiae in calcareus soil. Thailand, Annulohypoxylon spougei on corticated wood, Poaceascoma filiforme from leaves of unknown Poaceae. UK, Dendrostoma luteum on branch lesions of Castanea sativa, Ypsilina buttingtonensis from heartwood of Quercus sp. Ukraine, Myrmecridium phragmiticola from leaves of Phragmites australis. USA, Absidia pararepens from air, Juncomyces californiensis (incl. Juncomyces gen. nov.) from leaves of Juncus effusus, Montagnula cylindrospora from a human skin sample, Muriphila oklahomaensis (incl. Muriphila gen. nov.)on outside wall of alcohol distillery, Neofabraea eucalyptorum from leaves of Eucalyptus macrandra, Diabolocovidia claustri (incl. Diabolocovidia gen. nov.)from leaves of Serenoa repens, Paecilomyces penicilliformis from air, Pseudopezicula betulae from leaves of leaf spots of Populus tremuloides. Vietnam, Diaporthe durionigena on branches of Durio zibethinus and Roridomyces pseudoirritans on rotten wood. Morphological and culture characteristics are supported by DNA barcodes

Fungal Planet description sheets: 1042–1111

Novel species of fungi described in this study include those from various countries as follows: Antarctica, Cladosporium arenosum from marine sediment sand. Argentina, Kosmimatamyces alatophylus (incl. Kosmimatamyces gen. nov.) from soil. Australia, Aspergillus banksianus, Aspergillus kumbius, Aspergillus luteorubrus, Aspergillus malvicolor and Aspergillus nanangensis from soil, Erysiphe medicaginis from leaves of Medicago polymorpha, Hymenotorrendiella communis on leaf litter of Eucalyptus bicostata, Lactifluus albopicri and Lactifluus austropiperatus on soil, Macalpinomyces collinsiae on Eriachne benthamii, Marasmius vagus on soil, Microdochium dawsoniorum from leaves of Sporobolus natalensis, Neopestalotiopsis nebuloides from leaves of Sporobolus elongatus, Pestalotiopsis etonensis from leaves of Sporobolus jacquemontii, Phytophthora personensis from soil associated with dying Grevillea mccutcheonii. Brazil, Aspergillus oxumiae from soil, Calvatia baixaverdensis on soil, Geastrum calycicoriaceum on leaf litter, Greeneria kielmeyerae on leaf spots of Kielmeyera coriacea. Chile, Phytophthora aysenensis on collar rot and stem of Aristotelia chilensis. Croatia, Mollisia gibbospora on fallen branch of Fagus sylvatica. Czech Republic, Neosetophoma hnaniceana from Buxus sempervirens. Ecuador, Exophiala frigidotolerans from soil. Estonia, Elaphomyces bucholtzii in soil. France, Venturia paralias from leaves of Euphorbia paralias. India, Cortinarius balteatoindicus and Cortinarius ulkhagarhiensis on leaf litter. Indonesia, Hymenotorrendiella indonesiana on Eucalyptus urophylla leaf litter. Italy, Penicillium taurinense from indoor chestnut mill. Malaysia, Hemileucoglossum kelabitense on soil, Satchmopsis pini on dead needles of Pinus tecunumanii. Poland, Lecanicillium praecognitum on insects' frass. Portugal, Neodevriesia aestuarina from saline water. Republic of Korea, Gongronella namwonensis from freshwater. Russia, Candida pellucida from Exomias pellucidus, Heterocephalacria septentrionalis as endophyte from Cladonia rangiferina, Vishniacozyma phoenicis from dates fruit, Volvariella paludosa from swamp. Slovenia, Mallocybe crassivelata on soil. South Africa, Beltraniella podocarpi, Hamatocanthoscypha podocarpi, Coleophoma podocarpi and Nothoseiridium podocarpi (incl. Nothoseiridium gen. nov.)from leaves of Podocarpus latifolius, Gyrothrix encephalarti from leaves of Encephalartos sp., Paraphyton cutaneum from skin of human patient, Phacidiella alsophilae from leaves of Alsophila capensis, and Satchmopsis metrosideri on leaf litter of Metrosideros excelsa. Spain, Cladophialophora cabanerensis from soil, Cortinarius paezii on soil, Cylindrium magnoliae from leaves of Magnolia grandiflora, Trichophoma cylindrospora (incl. Trichophoma gen. nov.) from plant debris, Tuber alcaracense in calcareus soil, Tuber buendiae in calcareus soil. Thailand, Annulohypoxylon spougei on corticated wood, Poaceascoma filiforme from leaves of unknown Poaceae. UK, Dendrostoma luteum on branch lesions of Castanea sativa, Ypsilina buttingtonensis from heartwood of Quercus sp. Ukraine, Myrmecridium phragmiticola from leaves of Phragmites australis. USA, Absidia pararepens from air, Juncomyces californiensis (incl. Juncomyces gen. nov.) from leaves of Juncus effusus, Montagnula cylindrospora from a human skin sample, Muriphila oklahomaensis (incl. Muriphila gen. nov.)on outside wall of alcohol distillery, Neofabraea eucalyptorum from leaves of Eucalyptus macrandra, Diabolocovidia claustri (incl. Diabolocovidia gen. nov.)from leaves of Serenoa repens, Paecilomyces penicilliformis from air, Pseudopezicula betulae from leaves of leaf spots of Populus tremuloides. Vietnam, Diaporthe durionigena on branches of Durio zibethinus and Roridomyces pseudoirritans on rotten wood. Morphological and culture characteristics are supported by DNA barcodes