Let be the Laplace-d'Alembert operator on a pseudo-Riemannian manifold (M; g). We derive a series expansion for the fundamental solution G(x; y) of + H , H 2 C 1 (M), which behaves well under various symmetric space dualities. The qualitative properties of this expansion were used in our paper in Invent. Math. 129 (1997) 63{74, to show that the property of vanishing logarithmic term for G(x; y)...

Homomorphism duality pairs play a crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction that both classes are antichains. In ...

On classical phase spaces admitting just one complex–differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments ...

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...

A bstract I study generalisations of U-duality transformations which do not rely on the existence isometries. start by providing more details a recently proposed generalised map between solutions type IIA supergravity form M 7 × S 3 , with NSNS flux, and 11-dimensional supergravity, in three-sphere is replaced four-dimensional geometry encodes three-algebra structure constants. then show that w...

We derive a general relation between the bosonic and fermionic entanglement in ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications subsystems. Our derivation relies on unified framework to describe both, Gaussian terms so-called linear complex structures $J$. The resulting dualities apply full spectrum systems, such that von Neumann entropy a...