I. Bars et al., Noncommutative o(star)(N) and usp(star)(2N) algebras and the correspondinggauge field theories - art. no. 086004, PHYS REV D, 6408(8), 2001, pp. 6004
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.