Noncommutative o(star)(N) and usp(star)(2N) algebras and the correspondinggauge field theories - art. no. 086004

The extension of the noncommutative u(*)(N) Lie algebra to noncommutative o rthogonal and symplectic Lie algebras is studied. Using an antiautomorphism of the star-matrix algebra, we show that the u(*)(N) can consistently be r estricted to o(*)(N) and usp(*)(N) algebras that have new mathematical stru ctures. We give explicit fundamental matrix representations of these algebr as, through which the formulation for the corresponding noncommutative gaug e field theories are obtained. In addition, we present a D-brane configurat ion with an orientifold that realizes geometrically our algebraic construct ion, thus embedding the new noncommutative gauge theories in a superstring theory in the presence of a constant background magnetic field. Some algebr aic generalizations that may have applications in other areas of physics ar e also discussed.