Free differential algebras and generic 2D dilatonic (super)gravities

The field equations for both generic bosonic and generic locally supersymmetric 2D dilatonic gravity theories in the absence of matter are written as free differential algebras. This constitutes a generalization of the gauge theoretic formulation. Moreover, it is shown that the condition of free differential algebra can be used to obtain the equations in the locally supersymmetric case. Using this formulation, the general solution of the field equations is found in the language of differential forms. The relation with the ordinary formulation and the coupling to supersymmetric conformal matter are also studied.Comment: 19 pages, Late

On the coincidence between the Shimomuras bargaining sets and the core

A necessary condition for the coincidence of the bargaining sets dened by Shimomura (1997) and the core of a cooperative game with transferable utility is provided. To this aim, a set of payo vectors, called max-payo vectors, are introduced. This necessary condition simply checks whether these vectors are core elements of the game.max-payo vectors, core, bargaining set, cooperative games

Superalgebra cohomology, the geometry of extended superspaces and superbranes

We present here a cohomological analysis of the new spacetime superalgebras that arise in the context of superbrane theory. They lead to enlarged superspaces that allow us to write D-brane actions in terms of fields associated with the additional superspace variables. This suggests that there is an extended superspace/worldvolume fields democracy for superbranes.Comment: 12 pages, LATEX. Invited lecture delivered at the XXXVII Karpacz Winter School on "New Developments in Fundamental Interaction Theories" (6-15 February, 2001, Karpacz, Poland). To be published in the Proceeding

Hopf algebras with triality

In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and Zavarnitsine to groups with triality.Comment: AMS-LaTeX, 23 pages. To appear in Trans. Amer. Math. So

On Q6{\bf Q}_{6} flavor symmetry and the breaking of μ↔τ\mu \leftrightarrow \tau symmetry

In the simplest version of a $\mathbf{Q}_{6}$ flavored supersymmetric model, we analyze the leptonic masses and mixings in the framework of a soft breaking of the $\mu \leftrightarrow \tau$ symmetry. This breaking is controlled by the inequality $m_{e\tau}\neq m_{e\mu}$ in the effective neutrino mass. As a consequence of this breaking, the reactor and atmospheric angle are deviate from $0^{\circ}$ and $45^{\circ}$, respectively. Such deviations can be enhanced or suppressed by the CP parities in the Majorana phases, so that an analytic study is carried out to remark their importance to constrain the free parameters that accommodate the mixing angles. The normal hierarchy is completely discarded in this model, the inverted hierarchy is less favored than the degenerate one where the reactor and atmospheric angles are in good agreement with the experimental data. Additionally, the model predicts defined regions for the effective neutrino mass decay, the neutrino mass scale and the sum of the neutrino mass in the inverted and degenerate mass spectrum. Thus, this model may be testable by future experiments that focus in neutrinoless double beta decay.Comment: 21 pages, 20 figures. Improved version, new figures and references added. New section included. Conclusions unchanged. Version accepted for publication in International Journal of Modern Physics

Bosonic D=11 supergravity from a generalized Chern-Simons action

It is shown that the action of the bosonic sector of D=11 supergravity may be obtained by means of a suitable scaling of the originally dimensionless fields of a generalized Chern-Simons action. This follows from the eleven-form CS-potential of the most general linear combination of closed, gauge invariant twelve-forms involving the sp(32)-valued two-form curvatures supplemented by a three-form field. In this construction, the role of the skewsymmetric four-index auxiliary function needed for the first order formulation of $D=11$ supergravity is played by the gauge field associated with the five Lorentz indices generator of the bosonic sp(32) subalgebra of osp(1|32).Comment: Misprints corrected, to appear in NPB plain latex, no figures, 25 page