Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo
Sapienza Università di Roma
Settimana dal 9 al 15 luglio 2018
Giovedì 12 luglio 2018
Ore 16:00, aula 1B1, Dipartimento di Scienze di Base e Applicate per Ingegneria
(SBAI), via A. Scarpa 16
seminario di Algebre di Operatori
Jacopo Bassi
On C*-algebras associated to the action of discrete subgroups of SL(2,R)
on R2\{0}
Transformation group C*-algebras set up a connection between topological dynamics and the
theory of C*-algebras. In the case of discrete groups acting on compact spaces, many examples
have been considered so far for which it is possible to interpret dynamical properties on the
algebraic side and obtain classification results. The case of discrete groups acting on locally
compact non-compact spaces still deserves a proper study and some specific examples should be
investigated in order to make a first step in this direction.
In this talk I will focus on transformation group C*-algebras associated to the action of discrete
subgroups of SL(2,R) on R2\{0} by means of matrix multiplication of vectors.
I will introduce a weaker version of the 'wandering on compacts' assumption that is seen to guarantee
stability for a certain class of discrete subgroups of SL(2,R); in the case of cocompact subgroups
further structure results are obtained by looking at the C*-algebra associated to the horocycle flow
on the corresponding compact homogeneous space of SL(2,R). Based on the Preprint: arXiv:1806.09020v1
Giovedì 12 luglio 2018
Ore 17:00, aula 1B1, Dipartimento di Scienze di Base e Applicate per Ingegneria
(SBAI), via A. Scarpa 16
seminario di Algebre di Operatori
Luca Giorgetti
Minimal index and dimension for 2-C*-categories with finite-dimensional centers
The notion of index, in the sense we deal with in this talk, goes back to a seminal work of Jones on
subfactors of type II1. In the absence of a trace, one can still define the index of a conditional
expectation associated to a subfactor and look for expectations that minimize the index. This value is called
the minimal index of the subfactor. We report on our analysis of the minimal index for inclusions
of arbitrary von Neumann algebras (not necessarily finite, nor factorial) with finite-dimensional centers.
Our results generalize some aspects of the Jones’ index for multi-matrix inclusions (finite direct sums of matrix
algebras), e.g., the minimal index always equals the squared norm of a matrix, that we call matrix dimension,
as it is the case for multi-matrices with respect to the Bratteli or inclusion matrix. We shall discuss the
properties of this matrix dimension (multiplicativity and additivity, while the minimal index is neither
multiplicative nor additive beyond the subfactor case). We show how the theory of minimal index can be
formulated in the more general and purely algebraic context of 2-C*-categories.
Joint work with Roberto Longo (Roma Tor Vergata), preprint arxiv:1805.09234.
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