$QF-3'$ rings and Morita duality

Morita Duality and Large - N Limits

We study some dynamical aspects of gauge theories on noncommutative tori. We show that Morita duality, combined with the hypothesis of analyticity as a function of the non-commutativity parameter Θ, gives information about singular large-N limits of ordinary U (N) gauge theories, where the large-rank limit is correlated with the shrinking of a two-torus to zero size. We study some non-perturbat...

Strongly Rational Comodules and Semiperfect Hopf Algebras over QF Rings

Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right Ccomodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over...

Group - Graded Rings and Duality

We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known results on skew group rings to corresponding results for large classes of group-graded rings. Finally we modify the construction slightly to handle infinite groups. Introduction. In the first section...

Morita equivalence and T - duality ( or B versus

Morita equivalence and T - duality ( or B versus

Morita equivalence and T-duality (or B versus Θ) Abstract: T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM). Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant Abelian magnetic bac...