3 citations · 6 across the 10 of their papers we have counts for
13 papers
Ring theory in o-minimal structures
Annalisa Conversano
We develop a general ring theory in the o-minimal setting culminating in a description of all the definable rings in an arbitrary o-minimal structure. We show that every definably…
Definable rank, o-minimal groups, and Wiegold's problem
Annalisa Conversano
We show that an o-minimal structure M defines groups with infinite definable rank if and only if M defines some finite power of . If no interval of M is coun…
Lie groups in the symmetric group: reducing Ulam's problem to the simple case
Annalisa Conversano, Nicolas Monod
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we s…
A Jordan-Chevalley decomposition beyond algebraic groups
Annalisa Conversano
We prove a decomposition of definable groups in o-minimal structures generalizing the Jordan-Chevalley decomposition of linear algebraic groups. It follows that any definable linea…
Real Lie groups and o-minimality
Annalisa Conversano, Alf Onshuus, Sacha Post
We characterize, up to Lie isomorphism, the real Lie groups that are definable in an o-minimal expansion of the real field.
Groups definable in o-minimal structures: various properties and a diagram
Annalisa Conversano
We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-mini…
One Lie group to define them all
Annalisa Conversano, Marcello Mamino
We produce a connected real Lie group that, as a first order structure in the group language, interprets the real field expanded with a predicate for the integers. Moreover, the do…
Nilpotent groups, o-minimal Euler characteristic, and linear algebraic groups
Annalisa Conversano
We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal con…
Solvable Lie groups definable in o-minimal theories
Annalisa Conversano, Alf Onshuus, Sergei Starchenko
In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.
On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures
Annalisa Conversano, Anand Pillay
We study analogues of the notions from Lie theory of Levi subgroup and Levi decomposition, in the case of groups G definable in an o-minimal expansion of a real closed field. With…
Connected components of definable groups, and o-minimality II
Annalisa Conversano, Anand Pillay
We study the connected components G^00, G^000 and their quotients for a group G definable in a saturated o-minimal expansion of a real closed field. We show that G^00/G^000 is natu…
Connected components of definable groups and o-minimality I
Annalisa Conversano, Anand Pillay
We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably…
Lie-like decompositions of groups definable in o-minimal structures
Annalisa Conversano
There are strong analogies between groups definable in o-minimal structures and real Lie groups. Nevertheless, unlike the real case, not every definable group has maximal definably…