Back to the Amitsur–Levitzki Theorem: a Super Version for the Orthosymplectic Lie Superalgebra $${\mathfrak{o}}{\mathfrak{s}}{\mathfrak{p}}\left( {1,2n} \right)$$

We prove an Amitsur–Levitzki type theorem for the Lie superalgebras $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)$ ) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras $\mathfrak{g}\mathfrak{l}\left( {p,q} \right)$ cannot satisfy an Amitsur–Levitzki type super identity if pq≠0 and conjecture that neither can any other classical simple Lie superalgebra with the exception of $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)$ .     

Antioxidant capacity and in vitro prevention of dental plaque formation by extracts and condensed tannins of Paullinia cupana

Chemical evaluation of the semi-purified fraction from the seeds of guaraná, Paullinia cupana H.B.K. var. sorbilis (Mart.) Ducke, yielded the following compounds: caffeine, catechin, epicatechin, ent-epicatechin, and procyanidins B1, B2, B3, B4, A2, and C1. Measurement of the antioxidant activity by reduction of the DPPH radical confirmed the anti-radical properties of the aqueous (AqE) and crude (EBPC) extracts and semi-purified (EPA and EPB) fractions. The EPA fraction showed radical-scavenging activity (RSA) and protected DPPH from discoloration at 5.23 +/- 0.08 (RSD% = 1.49) microg/mL, and for the phosphomolybdenum complex showed a higher Relative Antioxidant Capacity (RAC) at 0.75 +/- 0.01 (1.75). The EPA fraction had a total polyphenolics content of 65.80% +/- 0.62 (RSD% = 0.93). The plant drug showed 5.47% +/- 0.19 (RSD% = 3.51) and 6.19% +/- 0.08 (RSD% = 1.29) for total polyphenolics and methylxanthines, respectively. In vitro assessment of the antibacterial potential of the Paullinia cupana extracts against Streptococcus mutans showed that these could be used in the prevention of bacterial dental plaque.     

A New Invariant of Quadratic Lie Algebras

We define a new invariant of quadratic Lie algebras and give a complete study and classification of singular quadratic Lie algebras, i.e. those for which the invariant does not vanish. The classification is related to O(n)-adjoint orbits in $\mathfrak{o}(n)$ .     

Electron spin density distribution in the polymer phase of CsC60: assignment of the NMR spectrum

We present high resolution 133Cs-13C double resonance NMR data and 13C-13C NMR correlation spectra of 13C enriched samples of the polymeric phase of CsC60. These data lead to a partial assignment of the lines in the 13C NMR spectrum of CsC60 to the carbon positions on the C60 molecule. A plausible completion of the assignment can be made on the basis of an ab initio calculation. The data support the view that the conduction electron density is concentrated at the C60 "equator," away from the interfullerene bonds.     

Supertrace and Superquadratic Lie Structure on the Weyl Algebra,and Applications to Formal Inverse Weyl Transform

Using the Moyal *-product and orthosymplectic supersymmetry, we construct a natural nontrivial supertrace and an associated nondegenerate invariant supersymmetric bilinear form for the Lie superalgebra structure of the Weyl algebra W. We decompose adjoint and twisted adjoint actions. We define a renormalized supertrace and a formal inverse Weyl transform in a deformation quantization framework and develop some examples Mathematics Subject Classification: 53D55, 17B05, 17B10, 17B20, 17B60, 17B65