Invariant States on Noncommutative Tori
| Autor: | Federico Bambozzi, Nicola Pinamonti, Simone Murro |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Symplectic group
General Mathematics Mathematics - Operator Algebras Sigma FOS: Physical sciences Torus Mathematical Physics (math-ph) 46L30 46L55 58B34 Bilinear form Noncommutative geometry Functional Analysis (math.FA) Mathematics - Functional Analysis Combinatorics Mathematics - Quantum Algebra FOS: Mathematics Ergodic theory Quantum Algebra (math.QA) Invariant (mathematics) Operator Algebras (math.OA) Mathematical Physics Mathematics |
| Popis: | 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 of $*$-automorphisms of $\mathcal{A}^h_{g,\sigma}$ induced by the action of the symplectic group Sp$(\mathbb{Z}^{2g},\sigma)$. We show that the only Sp$(\mathbb{Z}^{2g},\sigma)$-invariant state on $\mathcal{A}^h_{g,\sigma}$ is the trace state $\tau$. Comment: 11 pages - accepted in International Mathematics Research Notices |
| Databáze: | OpenAIRE |
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