Abstract
We describe the left regular module of a quantum complete intersection [Formula: see text] by the property that it is the unique finite-dimensional indecomposable left [Formula: see text]-module of Loewy length [Formula: see text] Using a reduction to [Formula: see text]-modules, we classify the [Formula: see text]-dimensional indecomposable left modules over quantum complete intersection [Formula: see text] in two variables, by explicitly giving their diagram presentations. Together with the existed work on indecomposable [Formula: see text]-modules of dimension [Formula: see text], we then know all the indecomposable [Formula: see text]-modules of dimension [Formula: see text].
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