Low dimensional modules over quantum complete intersections in two variables

Abstract

We classify all the indecomposable modules of dimension≤5 over the quantum exterior algebra k(x,y)/\langle x^{\mathrm{2}},y^{\mathrm{2}},xy+qyx\rangle in two variables, and all the indecomposable modules of dimension≤3 over the quantum complete intersection k(x,y)/\langle x^m,y^n,xy+qyx\rangle in two variables, where m or n≥3, by giving explicitly their diagram presentations.

Key words： Quantum exterior algebra; quantum complete intersection; diagram presentation of a module

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