A categorical approach to Weyl modules

Global and local Weyl modules were introduced via generators and relations in the context of affine Lie algebras in [CP2] and were motivated by representations of quantum affine algebras. In [FL] a more general case was considered by replacing the polynomial ring with the coordinate ring of an algebraic variety and partial results analogous to those in [CP2] were obtained. In this paper we show that there is a natural definition of the local and global Weyl modules via homological properties. This characterization allows us to define the Weyl functor from the category of left modules of a commutative algebra to the category of modules for a simple Lie algebra. As an application we are able to understand the relationships of these functors to tensor products, generalizing results in [CP2] and [FL]. We also analyze the fundamental Weyl modules and show that, unlike the case of the affine Lie algebras, the Weyl functors need not be left exact.     

Oleana‐12(13),15(16)‐diene‐3α,28‐diyl di­acetate

The title compound, C₃₄H₅₂O₄, consists of five six‐membered rings. Barring the two rings, with double bonds, all other rings are in chair conformations. Mean‐plane and ring‐puckering calculations indicate these two rings to be in distorted‐chair conformations, with distortion towards the boat conformation. There are no strong hydrogen bonds and the structure is stabilized by van der Waals interactions only. The structure is compared with those reported for other triterpenes.     

Pseudokobusine

The title compound, hetisan-6,11β,15β-triol, C₂₀H₂₇NO₃, is a hetisane-type diterpenoid alkaloid. It consists of six six-membered rings and two five-membered rings. The fused-ring system contains three chair, two boat, one distorted boat and two envelope conformations. Intramolecular and intermolecular hydrogen bonds are present between the O atoms, with O⃛O separations of 3.006 (3) and 2.743 (3) Å, as well as an O⃛N intermolecular interaction of 2.887 (3) Å.     

(24R)‐24,25‐Dihydroxycyclo­artan‐3‐one

In the title compound, C₃₀H₅₀O₃, the three six‐membered rings adopt chair, twist and twist‐boat conformations. The five‐membered ring is in a slightly distorted envelope conformation. The substituent on the five‐membered ring is in an extended conformation, with its two hydroxyl O atoms forming an intramolecular hydrogen bond. One of these O atoms also forms an intermolecular hydrogen bond with the oxy­gen of the carbonyl group in a neighbouring mol­ecule.     

Etch pit study of different crystallographic faces of L-arginine hydrobromide monohydrate (LAHBr) in alcohols

Chemical etchants based on simple alcohols were successfully applied for the first time to reveal dislocation sites on the polished {1 0 0}, {0 1 0}, {0 0 1} and {1 1 0} faces of L-arginine hydrobromide monohydrate. Fast dissolving etchants could produce etch pits only on the ‘F' faces but they have no effect on the ‘S' face. Selective behaviour of the etchants for revealing inclined dislocations and cooperating spirals has been demonstrated. Presence of growth spirals on {0 0 1} and {1 1 0} faces reveal that growth of these faces is governed by screw dislocation mechanism.     

Amino acids-precursors for synthesizing nonlinear optical materials

Some new nonlinear optical materials were synthesized from amino acids l-arginine and l-valine and single crystals were grown from their aqueous solution by solvent evaporation method at constant temperature and slow cooling method. The synthesized materials were identified by carbon, hydrogen, nitrogen (CHN) test and single crystal X-ray diffraction (XRD) analysis. The grown crystals were characterized by measuring their thermal, optical and mechanical properties by Differential Thermal Analysis (DTA), Thermo Gravimetric Analysis (TGA), powder second harmonic generation (SHG) efficiency, damage threshold and microhardness measurements. Our study shows that halides of l-arginine and l-valine are promising Nonlinear Optical (NLO) materials having Second Harmonic Generation (SHG) efficiency, mechanical and thermal stability greater than other semi-organic NLO materials. But among the halide salts, l-valine hydrobromide (LVHBr) emerged as most promising NLO materials as far as SHG efficiency, and damage threshold are concerned.     

Dislocation structure and microhardness of L-arginine perchlorate single crystal

This paper presents the chemical etching and microhardness studies carried out on L-arginine perchlorate (LAPCl), a non-linear optical crystal (NLO) with a view to characterize the dislocation structure and mechanical strength of the grown crystals. LAPCl crystals employed in this investigation were grown from aqueous solution by solvent evaporation method. Optical microscopic studies of as grown habit faces revealed formation of macrosteps and valley on (100) habit face. Chemical etching of (100) face with impurity added organic solvents played an important role in the formation of etch pits. Selective etching of matched pairs on opposite faces of the same plane confirms that the pits are formed at the dislocation sites. Microhardness measurement by indentation method shows decrease of microhardness with increasing load. Nature of hardness profile is explained with the help of Meyer’s law. The work hardening index value indicates that LAPCl belongs to hard crystal category.     

Synthesis,growth and characterization of a new nonlinear optical crystal: l‐arginine maleate dihydrate

A new nonlinear optical material L‐arginine maleate dihydrate, C₆H₁₄N₄O₂,C₄H₄O₄,2H₂O (LAMD) was synthesized and single crystals were grown by slow cooling and also by slow evaporation method at constant temperature from its aqueous solution. Quality and size of the crystals are found to be dependent on pH of the solution and best crystals were obtained at pH = 4. Single crystal X‐ray diffraction analysis reveal that the crystal lattice of LAMD is triclinic with unit cell parameters a = 5.264(3)Å, b = 8.039(3)Å, c = 9.784(3)Å, α = 106.19(3)°, β = 97.24(3)°, γ = 101.66(2)°. Second harmonic generation efficiency is found to be about 6.8 times that of quartz. It is optically transparent down to 300 nm and possesses a large optical window between 300–2000 nm. The compound is thermally stable up to 93.4 °C. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)