The Balian–Low theorem and noncommutative tori
Sign Up to like & getrecommendations! Published in 2018 at "Expositiones Mathematicae"
DOI: 10.1016/j.exmath.2018.03.003
Abstract: We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor-Riesz bases and a constant curvature connection on projective modules over noncommutative tori. read more here.
Keywords: theorem noncommutative; low theorem; balian low; noncommutative tori ... See more keywords
The Riemann–Roch Theorem on higher dimensional complex noncommutative tori
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2019.103534
Abstract: Abstract We prove analogues of the Riemann–Roch Theorem and the Hodge Theorem for noncommutative tori (of any dimension) equipped with complex structures, and discuss implications for the question of how to distinguish “noncommutative abelian varieties”… read more here.
Keywords: riemann roch; noncommutative tori; theorem; roch theorem ... See more keywords
Invariant States on Noncommutative Tori
Sign Up to like & getrecommendations! Published in 2019 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnz189
Abstract: For any number $h$ such that $\hbar :=h/2\pi $ is irrational and any skew-symmetric, non-degenerate bilinear form $\sigma :{{\mathbb{Z}}}^{2g}\times{{\mathbb{Z}}}^{2g} \to{{\mathbb{Z}}}$, let be ${{\mathcal{A}}}^h_{g,\sigma }$ be the twisted group *-algebra ${{\mathbb{C}}}[{{\mathbb{Z}}}^{2g}]$ and consider the ergodic group… read more here.
Keywords: mathcal sigma; states noncommutative; sigma; noncommutative tori ... See more keywords