  The extension of the noncommutative u*(N) Lie algebra to noncommutative
orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism
of the star-matrix algebra, we show that the u*(N) can consistently be
restricted to o*(N) and usp*(N) algebras that have new mathematical structures.
We give explicit fundamental matrix representations of these algebras, through
which the formulation for the corresponding noncommutative gauge field theories
are obtained. In addition, we present a D-brane configuration with an
orientifold which realizes geometrically our algebraic construction, thus
embedding the new noncommutative gauge theories in superstring theory in the
presence of a constant background magnetic field. Some algebraic
generalizations that may have applications in other areas of physics are also
discussed.
