# Invariant states on Weyl algebras for the action of the symplectic group

@article{Bambozzi2018InvariantSO, title={Invariant states on Weyl algebras for the action of the symplectic group}, author={Federico Bambozzi and Simone Murro and Nicola Pinamonti}, journal={arXiv: Operator Algebras}, year={2018} }

For any number h such that hbar:=h/(2\pi) is irrational, let A_{g,h} be the corresponding Weyl *-algebra over Z^{2g} and consider the ergodic group of *-automorphisms of A_{g,h} induced by the action of Sp(2g,Z) on Z^{2g}. We show that the only Sp(2g,Z)-invariant state on A_{g,h} is the trace state.

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