Morita equivalence and T - duality ( or B versus

Morita equivalence and T - duality ( or B versus

Morita Equivalence in Algebra and Geometry

We study the notion of Morita equivalence in various categories. We start with Morita equivalence and Morita duality in pure algebra. Then we consider strong Morita equivalence for C-algebras and Morita equivalence for W-algebras. Finally, we look at the corresponding notions for groupoids (with structure) and Poisson manifolds.

T-duality of non-commutative gauge theories

Via T-duality a theory of open strings on a D1-brane wrapped along a cycle of slanted torus is described by a U(1) gauge theory on a D2-brane in the B-field background. It is also known that there is another dual description of the D1-brane configuration by a non-commutative gauge theory on a D2-brane. Therefore, these two gauge theories on D2-branes are equivalent. Recently, the existence of a...

ar X iv : h ep - t h / 98 11 15 9 v 2 1 0 D ec 1 99 8 BPS states on noncommutative tori and duality

We study gauge theories on noncommutative tori. It was proved in [5] that Morita equivalence of noncommutative tori leads to a physical equivalence (SO(d, d|Z)-duality) of the corresponding gauge theories. We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the SO(d, d|Z)-duality. The relation of our results with thos...

On Morita theory for self-dual modules

Let G be a finite group and let k be a field of characteristic p. It is known that a kG-module V carries a non-degenerate G-invariant bilinear form b if and only if V is self-dual. We show that whenever a Morita bimodule M which induces an equivalence between two blocks B(kG) and B(kH) of group algebras kG and kH is self-dual then the correspondence preserves self-duality. Even more, if the bil...