[en] The decomposition of representations of supergroups into representations of subgroups is needed in practical applications. In this paper we set up and exploit a fruitful one-to-one correspondence between the Lie group branching SU (N+M)containsSU(N)xSU(M)xU(1) and the supergroup branchings SU(N/M)containsSU(N)xSU(M)xU(1) and SU(N₁+N₂/M₁+M₂)containsSU(N₁/M₁) xSU(N₂/M₂)xU(1). A simple and useful prescription is discovered for obtaining the SU(N/M) branching rules from those of SU(N+M) for any representation. A large class of examples, sufficient for many physical applications we can foresee, are explicitly worked out and tabulated

[en] It is shown that the true supergravity group is a unification of two complex conjugated general covariance groups in two smaller ''chiral'' superspaces, the left-handed one and the rio.ht-handed one. The gravitational superfield is introduced as the imaginary part of the complex space-time coordinate in our complex superspace, while the real part is identified with the true space coordinate. Simultaneously, the gravitational superfield is a ''metric'' object of the real subspace. In this way, a simple and clear geometrical picture of the supergravity group is obtained. A generalization to extended supergravity is straightforward. (author)

[en] A mathematically consistent global theory of super fibre bundles is laid down. In this framework one may perform, in a rigorous way, the analysis of the construction of super fibre bundles, connections, reduced bundles and reduced connections. Some bundles of physical interest, constructed over a supermanifold are analysed in detail. A criterion for the existence of a Lorentz bundle over a a supermanifold is established. Some results about subgroups of super Lie groups are also given. (author)

[en] Motivated by the recent proposal of an N = 8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also discuss the application of Lie 3-algebra to the membrane physics, including the Basu-Harvey equation and the Bagger-Lambert model.

[en] In this short note we list possible representations of the classical semisimple groups G₁xG₂ for finite N=2 supersymmetric theories. (orig.)

[en] We investigate space-time supersymmetry of the model of multiple M2-branes proposed by Bagger-Lambert and Gustavsson. When there is a central element in Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in the central element. Together with the original worldvolume supersymmetry transformation, we construct major part of the eleven dimensional space-time super-Poincare algebra with central extensions. Implications to transverse five-branes in the matrix model for M-theory are also discussed.

[en] In this paper, we construct the additional symmetries of the supersymmetric BKP (SBKP) hierarchy. These additional flows constitute a B type ${\mathit{SW}}_{1+\infty }$ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy. Further we generalize the SBKP hierarchy to a supersymmetric two-component BKP (S2BKP) hierarchy equipped with a B type ${\mathit{SW}}_{1+\infty }⨁{\mathit{SW}}_{1+\infty }$ Lie algebra. As a bosonic reduction of the S2BKP hierarchy, we define a new constrained system called the supersymmetric Drinfeld–Sokolov hierarchy of type D which admits a $N=2$ supersymmetric Block type symmetry.

[en] Short note. 2 refs

[en] In this paper, a supersymmetric extension of the polytropic gas dynamics equations is constructed through the use of a superspace involving two independent fermionic variables and two bosonic superfields. A superalgebra of symmetries of the proposed extended model is determined and a systematic classification of the one-dimensional subalgebras of this superalgebra is performed. Through the use of the symmetry reduction method, a number of invariant solutions of the supersymmetric polytropic gas dynamics equations are found. Several types of solutions are obtained including algebraic-type solutions and propagation waves (simple and double waves). Many of the obtained solutions involve arbitrary functions of one or two bosonic or fermionic variables. In the case where the arbitrary functions involve only the independent fermionic variables, the solutions are expressed in terms of Taylor expansions.

No abstract available