No abstract available

[en] A method for evaluation of matrix elements of unitary irreducible representations of compact Lie groups is formulated. Matrix elements of some representations of the group SO(p + q) in the SO(p) x SO(q) basis and of the group U(p) x U(p) in the U(p) basis (diagonal imbedding) are given. (orig.)

[en] Short communication

[en] Let tsub(n) (+ u(n) be the semi-direct sum of an abelian Lie algebra with the Lie algebra of unitary group U(n). It is shown that an invariant of u(n+1) is also an invariant of tsub(n)(+ u(n) if phi:tsub(n)(+ u→u(n+1) is an expansion. Sixth-order invariants of semi-direct sum algebra are calculated by this method

[en] Short note. 1 tab

[en] For a right-invariant system on a compact Lie group G, I present two methods to design a control to drive the state from the identity to any element of the group. The first method, under appropriate assumptions, achieves exact control to the target but requires estimation of the 'size' of a neighborhood of the identity in G and solution of a nonlinear algebraic equation. The second method does not involve any mathematical difficulty and obtains control to a desired target with arbitrary accuracy. A third method is then given combining the main ideas of the previous methods. This is also very simple in its formulation and turns out to be generically more efficient as illustrated by one of the examples I consider. The methods described in the paper provide arbitrary constructive control for any right-invariant system on a compact Lie group. In particular, the results can be applied to the coherent control of general multilevel quantum systems to an arbitrary target.

[en] The discrete orthogonality of special function families, called C- and S-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivnák and Patera (2009 J. Phys. A: Math. Theor. 42 385208). Here, the results of Hrivnák and Patera are extended to two additional recently discovered families of special functions, called S^s- and S^l-functions. The main result is an explicit description of their pairwise discrete orthogonality within each family, when the functions are sampled on finite fragments F^s_M and F^l_M of a lattice in any dimension n ⩾ 2 and of any density controlled by M, and of the symmetry of the weight lattice of any compact simple Lie group with two different lengths of roots. (paper)

[en] The graded Poincare (GP) Lie algebra of supersymmetry is examined with a view to constructing possible affine extensions of the algebra, i.e., extensions of the GP algebra which contain as a subalgebra the Lie algebra ga(4,R). Attention is restricted to an examination of the finite extensions. It is explicitly demonstrated that if only a symmetric tensor generator is adjoined to the GP algebra, then such a generator cannot generate all the deformations, in particular the shear, of the general affine group GA(4,R). Similarly, it is shown that adjoining the supersymmetry generator to ga(4,R) cannot lead to closure of the resulting algebra, even in the trivial case. It is further demonstrated that the GLA ga(4/4, R) does not contain the Lie algebra ga(4,R) represented over the entire superspace upon which ga(4/4, R) is defined

[en] Crystal structures of the LpxA protein from A. baumannii were solved in apo forms that were suitable for structure-based antibacterial drug discovery. Acinetobacter baumannii is a Gram-negative pathogenic bacterium which is resistant to most currently available antibiotics and that poses a significant health threat to hospital patients. LpxA is a key enzyme in the biosynthetic pathway of the lipopolysaccharides that are components of the bacterial outer membrane. It is a potential target for antibacterial agents that might be used to fight A. baumannii infections. This paper describes the structure determination of the apo form of LpxA in space groups P2₁2₁2₁ and P6₃. These crystal forms contained three and one protein molecules in the asymmetric unit and diffracted to 1.8 and 1.4 Å resolution, respectively. A comparison of the conformations of the independent protein monomers within and between the two crystal asymmetric units revealed very little structural variation across this set of structures. In the P6₃ crystal form the enzymatic site is exposed and is available for the introduction of small molecules of the type used in fragment-based drug discovery and structure-based lead optimization

[en] The structure of T. gondii fructose-1,6-bisphosphate aldolase, a glycolytic enzyme and structural component of the invasion machinery, was determined to a resolution of 2.0 Å. The apicomplexan parasite Toxoplasma gondii must invade host cells to continue its lifecycle. It invades different cell types using an actomyosin motor that is connected to extracellular adhesins via the bridging protein fructose-1,6-@@bisphosphate aldolase. During invasion, aldolase serves in the role of a structural bridging protein, as opposed to its normal enzymatic role in the glycolysis pathway. Crystal structures of the homologous Plasmodium falciparum fructose-1,6-bisphosphate aldolase have been described previously. Here, T. gondii fructose-1,6-bisphosphate aldolase has been crystallized in space group P22₁2₁, with the biologically relevant tetramer in the asymmetric unit, and the structure has been determined via molecular replacement to a resolution of 2.0 Å. An analysis of the quality of the model and of the differences between the four chains in the asymmetric unit and a comparison between the T. gondii and P. falciparum aldolase structures is presented