Year: 2025
Type: article
Abstract: The set of spreadable states on an infinite non-commutative torus A α Z \mathbb {A}_\alpha ^\mathbb {Z} is determined for all values of the deformation parameter α \alpha . If α 2 π \frac {\alpha }{2\pi } is irrational, the canonical trace is the only spreadable state. If α 2 π \frac {\alpha }{2\pi } is rational, the set of all spreadable states is a Bauer simplex. Moreover, its boundary is the set of all infinite products of a single state on C ( T ) C(\mathbb {T}) , which is invariant under all rotations by n 0 n_0 -th roots of unity, where n 0 = p 1 { m 1 2 } … p r { m r 2 } n_0=p_1^{\{\frac {m_1}{2}\}}\dots p_r^{\{\frac {m_r}{2}\}} , with { n 2 } \{\frac {n}{2}\} being n 2 \frac {n}{2} for
DOI: 10.1090/proc/17490
Institution: University of Bari Aldo Moro
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3667887601
OpenAlex ID: W4417167528