arXiv subjects
Publications and source records attributed to P. Sancho.
Finite modules, finitely presented modules and Mittag-Leffler modules are characterized by their behaviour by tensoring with direct products of modules. In this paper, we study and characterize the functors of modules that preserve direct products.
We present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic Lie groups.
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.
A functor of sets $\mathbb X$ over the category of $K$-commutative algebras is said to be an affine functor if its functor of functions, $\mathbb A_{\mathbb X}$, is reflexive and $\mathbb X=\Spec \mathbb A_{\mathbb X}$. We prove that affine functors are equal to a direct limit of affine schemes and that affine schemes, formal schemes, the completion of affine schemes along a closed subscheme, etc., are affine functors. Endowing an affine functor $\mathbb X$ with a functor of monoids structure is equivalent to endowing $\mathbb A_{\mathbb X}$ with a functor of bialgebras structure. If $\mathbb G$ is an affine functor of monoids, then $\mathbb A_{\mathbb G}^*$ is the enveloping functor of algebras of $\mathbb G$ and the category of $\mathbb G$-modules is equivalent to the category of $\mathbb A_{\mathbb G}^*$-modules. Applications of these results include Cartier duality, neutral Tannakian duality for affine group schemes, the equivalence between formal groups and Lie algebras in characteristic zero, etc.
Multimode two-particle systems show interference effects in one-particle detections when both particles have common modes. We explore the possibility of extending the usual concepts of distinguishability and visibility to these types of systems. Distinguishability will refer now to the balance between common and different modes of a two-particle system, instead of the standard definition concerning available alternatives for a one-particle system. On the other hand, the usual concept of visibility is not suitable for our problem and must be replaced with that of contrast, measuring the ratio of detection probabilities with and without interference effects. Finally, we show that for the type of states considered in the paper there is a complementarity relation between distinguishability and contrast for two-bosons systems. In contrast, there is no two-fermion counterpart.