We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters ...

We give a definition and study Hopf structures in ternary ( and n-ary) NambuLie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra and Hopf 3algebra are introduced. Some examples of Hopf structures are analyzed. Mathematics Subject Classification (1991) 70H99, 58F07 1 [email protected] 2 [email protected] In 1973 Yoishira Nambu [1] proposed a generalization of classical Hamiltonian mecha...

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-P...

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-P...

Wave maps (i.e. nonlinear sigma models) with torsion are considered in 2+1 dimensions. Global existence of smooth solutions to the Cauchy problem is proven for certain reductions under a translation group action: invariant wave maps into general targets, and equivariant wave maps into Lie group targets. In the case of Lie group targets (i.e. chiral models), a geometrical characterization of inv...

Thirteen newly isolated monoclonal antibodies (MAbs) were used to study relationships between reovirus outer capsid proteins sigma 3, mu 1c, and lambda 2 (core spike) and the cell attachment protein sigma 1. We focused on sigma 1-associated properties of serotype specificity and hemagglutination (HA). Competition between MAbs revealed two surface epitopes on mu 1c that were highly conserved bet...

New data are presented on the phase equilibria and crystal chemistry of the binary systems Sr0-Bi203 and SrO-CuO and the ternary system SrO-Bi2O3-CuO. Symmetry data and unit cell dimensions based on single crystal and powder x-ray diffraction measurements are reported for all the binary SrO-Bi2O3 phases, including a new phase identified as Sr6Bi2O9. The ternary system contains at least four ter...