210 citations · 464 across the 57 of their papers we have counts for
69 papers
Solution to Dixmier's Problem about spectra of C*-algebras
Martino Lupini
Dixmier asked in 1967 whether the spectra of simple separable non-type-I -algebras all have the same Borel structure. We solve the formulation using ordinary isomorphisms of q…
The universal valued Abelian groups of Niemiec are Lévy, strongly exotic, extremely amenable, and is generically monothetic
Alessandro Codenotti, Martino Lupini
We prove various properties of the universal valued Abelian groups constructed by Niemiec, for and . First we show that t…
The Exact Completion of the Category of Polish Groups
Martino Lupini
This article shows that the exact completion as a regular category of the homological category of Polish groups and continuous group homomorphisms is the category of groups with a…
The Borel complexity of non-Archimedean operator ranges
Martino Lupini
We completely classify the possible complexity classes of non-closed operator ranges on separable Banach spaces over a Polish non-Archimedean non-trivially valued field. These are…
Polarities, voltages, and capacitors: a categorical approach to hulls, envelopes, and completions
Ivan Di Liberti, Martino Lupini
This article provides a general framework in the context of category theory where one can recognize as particular instances of the same abstract construction several notions of com…
Applications of Borel-definable homological algebra to locally compact groups
Martino Lupini
We apply the description of the left heart of the category of locally compact Polish abelian groups in terms of groups with a Polish cover and Borel-definable grou…
A new characterization of (pre)liminary C*-algebras
Martino Lupini
Given an arbitrary countable ordinal , we introduce the notion of type C*-algebra and -subhomogeneous C*-algebra. When , these recover the notions of Fell C*-alg…
Derivation length and automorphism length of unital C*-algebras
Martino Lupini
This paper is a contribution to the study of the ordinal-valued invariants of derivation and automorphism length. Akemann--Pedersen and Elliott proved that a separable unital C*-al…
Projective length, phantom extensions, and the structure of flat modules
Matteo Casarosa, Martino Lupini
We consider the natural generalization of the notion of the order of a phantom map from the topological setting to triangulated categories. When applied to the derived category of…
Homological algebra of pro-Lie Polish abelian groups
Matteo Casarosa, Alessandro Codenotti, Martino Lupini
In this paper, we initiate the study of pro-Lie Polish abelian groups from the perspective of homological algebra. We extend to this context the type-decomposition of locally compa…
The definable content of homological invariants II: Čech cohomology and homotopy classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebr…
The classification problem for extensions of torsion-free abelian groups, I
Martino Lupini
Let be countable abelian groups. In this paper we determine the complexity of classifying extensions by , in the cases when is torsion-free and is a -group,…
Complexity classes of Polishable subgroups
Martino Lupini
In this paper we further develop the theory of canonical approximations of Polishable subgroups of Polish groups, building on previous work of Solecki and Farah--Solecki. In partic…
(Looking For) The Heart of Abelian Polish Groups
Martino Lupini
We prove that the category of abelian groups with a Polish cover introduced in collaboration with Bergfalk and Panagiotopoulos is the left heart of (the derived categ…
Computable topological abelian groups
Martino Lupini, Alexander Melnikov, Andre Nies
We study the algorithmic content of Pontryagin - van Kampen duality. We prove that the dualization is computable in the important cases of compact and locally compact totally disco…
Projective length, phantom extensions, and the structure of torsion modules
Martino Lupini
The notion of phantom extension of order a given ordinal has been introduced in collaboration with Casarosa, as an algebraic analogue of the order of a phantom map in topology,…
A general Universal Coefficient Theorem, and applications
Luigi Caputi, Martino Lupini
In this paper we isolate a general Universal Coefficient Theorem in the context of abelian categories. We then apply it in the left heart of the quasi-abelian category of abelian P…
Definable -homology of separable C*-algebras
Martino Lupini
In this paper we show that the -homology groups of a separable C*-algebra can be enriched with additional descriptive set-theoretic information, and regarded as definab…
The definable content of homological invariants I: &
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the first installment in a series of papers in which we illustrate how classical invariants of homological algebra and algebraic topology can be enriched with additional de…
The Ramsey property for Operator spaces and noncommutative Choquet simplices
Dana Bartošová, Jordi Lopez-Abad, Martino Lupini +1
The noncommutative Gurarij space , initially defined by Oikhberg, is a canonical object in the theory of operator spaces. As the Fra\"ıssé limit of t…
Dilation theory in finite dimensions and matrix convexity
Michael Hartz, Martino Lupini
We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as a general…
The Ramsey properties for Grassmannians over ,
Dana Bartošová, Jordi Lopez-Abad, Martino Lupini +1
In this note we study and obtain factorization theorems for colorings of matrices and Grassmannians over and , which can be considered metric versions of…
Definable (co)homology, pro-torus rigidity, and (co)homological classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
We show that the classical homology theory of Steenrod may be enriched with descriptive set-theoretic information. We prove that the resulting definable homology theory provides a…
On Rado conditions for nonlinear Diophantine equations
Jordan Mitchell Barrett, Martino Lupini, Joel Moreira
Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired…