Related papers: Morita equivalence and duality

We prove that two cusps of the same dimension in the Baily-Borel compactification of some classical series of modular varieties are linearly dependent in the rational Chow group of the compactification. This gives a higher dimensional…

We study Morita theory of twisted sheaves on $\mu_{n}$-gerbes of line bundles $\mathscr{X}$. In this context, we find explicit equivalent conditions for when two Azumaya algebras on $\mathscr{X}$ are Morita equivalent. Additionally, we…

This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In \cite{mem} we introduced the basic DG category $\Pc_{\A^\bullet}$, the perfect category…

Let N_1 (resp.N_2) be a nest A (resp. B) be the corresponding nest algebra, A_0 (resp. B_0) be the subalgebra of compact operators. We prove that the nests N_1, N_2 are isomorphic if and only if the algebras A, B are weakly-* Morita…

In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between noncommutative field theories and deformed vector bundles which give the Morita equivalence…

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the…

We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C. We prove that two…

We consider the compactification of M theory on a light-like circle as a limit of a compactification on a small spatial circle boosted by a large amount. Assuming that the compactification on a small spatial circle is weakly coupled type…

After embedding the objects quasifolds into the category {Diffeology}, we associate a C*-agebra with every atlas of any quasifold, and show how different atlases give Morita equivalent algebras. This builds a new bridge between diffeology…

We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…

Many important ideas about string duality that appear in conventional $\T^2$ compactification have analogs for $\T^2$ compactification without vector structure. We analyze some of these issues and show, in particular, how orientifold planes…

We prove that two dual operator algebras are weak$^*$ Morita equivalent if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak$^*$-continuous on appropriate morphism…

We develop methods to study the singularities of certain $G_2$ cones related to toric hyperkahler spaces and Einstein selfdual orbifolds. This allows us to determine the low energy gauge groups of chiral N=1 compactifications of M-theory on…

We prove the existence of a Mori contraction on a compact Kaehler threefold whose canonical bundle is (analytically) not nef if the threefold can be approximated by projective threefolds or if the algebraic dimension is 2.

The global analytic hypoellipticity is proved for a class of second order partial differential equations with non-negative characteristic form globally defined on the torus. The class considered in this work generalizes at some degree the…

We study the Matrix theory description of M-theory compactified on $T^4$ and $T^5$. M-theory on $T^4$ is described by the six dimensional (2,0) fixed point field theory compactified on a five torus, $\widetilde T^5$. For M-theory on $T^5$…

We extend categorical Morita equivalence to finite tensor categories graded by a finite group $G$. We show that two such categories are graded Morita equivalent if and only if their equivariant Drinfeld centers are equivalent as braided…

We consider the dimensional reduction/compactification of supergravity, string and M-theories on tori with one time-like circle. We find the coset spaces in which the massless scalars take their values, and identify the discrete duality…

It is shown that many of the conjectured dualities involving orbifold compactification of M-theory follow from the known dualities involving M-theory and string theory in ten dimensions, and the ansatz that orbifolding procedure commutes…

This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…