We construct an explicit example of a generalized Lie 3-algebra from the octonions. In combination with the result of [1], this gives rise to a three-dimensional N = 2 Chern-Simons-matter theory with exceptional gauge group G2 and with global symmetry SU(4) × U(1). This gives a possible candidate for the theory on multiple M2-branes with G2 gauge symmetry.

The Co(II) atom in the title salt, (C(10)H(18)N)(2)[CoCl(4)], exists in a tetra-hedral coordination geometry. The asymmetric unit has two cations that lie on different special positions of site symmetry m; the anion lies on another special position of site symmetry m.

The topological eld theories associated with a ne Lie superalgebras are constructed. Their BRST symmetry is characterised by a Kazama algebra containing spin 1, 2 and 3 operators and closes linearly. Under this symmetry all operators are grouped into BRST doublets. The relation between the models constructed and non-critical string theories is explored.

In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasitriangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homo...

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations.

In the crystal structure of the title compound, C(24)H(6)O, the mol-ecule exhibits point symmetry m but the mirror plane is not utilized as part of the space-group symmetry. The structure contains face-to-face inter-actions between the 2,4-dimethyl-benzyl-idene substituents in which the methyl groups lie directly above the centroids of adjacent benzene rings.

‎let $l$ be a lie algebra‎, ‎$mathrm{der}(l)$ be the set of all derivations of $l$ and $mathrm{der}_c(l)$ denote the set of all derivations $alphainmathrm{der}(l)$ for which $alpha(x)in [x,l]:={[x,y]vert yin l}$ for all $xin l$‎. ‎we obtain an upper bound for dimension of $mathrm{der}_c(l)$ of the finite dimensional nilpotent lie algebra $l$ over algebraically closed fields‎. ‎also‎, ‎we classi...

In 1935, G. I. Taylor invoked rotational symmetry to derive a remarkable formula for the turbulent dissipation rate. That derivation, though ingenious, leaves it unclear if truly conforms with symmetry. We use machinery of Lie groups furnish rigorous derivation Taylor's under and also not considered by Taylor, reflectional

A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type A4. Similar crystals wit...