Invariants of the quantum torus (Q986506)

The quantum torus is an algebra generated by two elements \(x\) and \(y\) subject to relation \(yx=qxy\) where \(q\) is a complex number. In this article an action of the group \(\mathrm{SL}(2,\mathbb{Z})\) on quantum torus is defined and invariants of finite sub-groups of this group are studied. In particular, \(0\)-degree Hochschild homology of these sub-algebras of invariants are computed.