Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

Development of a spectrophotometric Sequential Injection Analysis (SIA) procedure for determination of ammonium: A Response Surface Methodology (RSM) approach

This paper describes the optimization and use of a Sequential Injection Analysis (SIA) procedure for ammonium determination in waters. Response Surface Methodology (RSM) was used as a tool for optimization of a procedure based on the modified Berthelot reaction. The SIA system was designed to (i) prepare the reaction media by injecting an air-segmented zone containing the reagents in a mixing chamber, (ii) to aspirate the mixture back to the holding coil after homogenization, (iii) drive it to a thermostated reaction coil, where the flow is stopped for a previously established time, and (iv) to pump the mixture toward the detector flow cell for the spectrophotometric measurements. Using a 100 mu mol L(-1) ammonium solution, the following factors were considered for optimization: reaction temperature (25 - 45 degrees C), reaction time (30 - 90 s), hypochlorite concentration (20 - 40 mmol L(-1)) nitroprusside concentration (10 - 40 mmol L(-1)) and salicylate concentration (0.1 - 0.3 mol L(-1)). The proposed system fed the statistical program with absorbance data for fast construction of response surface plots. After optimization of the method, figures of merit were evaluated, as well as the ammonium concentration in some water samples. No evidence of statistical difference was observed in the results obtained by the proposed method in comparison to those obtained by a reference method based on the phenol reaction. (C) 2010 Elsevier B.V. All rights reserved.

Excited-state dynamics of polyfluorene derivatives in solution

The excited-state dynamics of two polyfluorene copolymers, one fully conjugated containing phenylene vinylene units alternated with 9,9`-dihexylfluorenyl groups and the other segmented by -(CH2)(8)- spacer, were studied in dilute solution of different solvents using a picosecond single-photon timing technique. The excited-state dynamics of the segmented copolymer follows the Forster resonant energy-transfer model which describes intrachain energy-transfer kinetics among random oriented chromophores. Energy transfer is confirmed by analysis of fluorescence anisotropy relaxation with the measurement of a short decay component of about 60 ps. The fluorescence decay surface of the fully conjugated copolymer is biexponential with decay times of about 470 and 900 ps, ascribed to deactivation of chain moieties containing trans and cis isomers already in a photostationary condition. Thus, energy transfer is very fast due to the conjugated nature and rigid-rod-like structure of this copolymer chain.

Effect of polyol excess on the electrical property of vegetable-polyurethane film

Freestanding castor oil-based polyurethane (PU) film was obtained using spin-coating method. The effect of polyol content was analysed by means of thermally stimulated depolarisation current and AC dielectric measurements techniques. Two relaxation peaks were observed in the temperature range of -40 to 60 degrees C for PU with different polyol contents. The presence of polyol excess provides a shift to lower temperature of the a relaxation and the decrease in the activation energy of the transition in this region might be attributed to the plasticising effect of the polyol. The peak at higher temperature is due to the Maxwell-Wagner-Sillars relaxation, which also shifts in the low temperature direction as the polyol content is increased.