Compactification of M(atrix) theory on noncommutative toroidal orbifolds

It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative to ri arise naturally in consideration of toroidal compactifications of M(atri x) theory. A similar analysis of toroidal Z(2) orbifolds leads to the algeb ra B-theta that can be defined as a crossed product of noncommutative torus and the group Z(2). Our paper is devoted to the study of projective module s over B-theta (Z(2)-equivariant projective modules over a noncommutative t orus), We analyze the Morita equivalence (duality) for B-theta algebras wor king out the two-dimensional case in detail. (C) 2000 Elsevier Science B.V. All rights reserved.