Wei-Heng Xia

The Auslander--Reiten conjecture for quantum complete intersections

Let \(A\) be a finite-dimensional quantum complete intersection over an arbitrary field. We prove that a finite-dimensional left \(A\)-module \(M\) is projective whenever \(\Ext_A^1(M,M)=\Ext_A^2(M,M)=0\), with no restriction on the multiplicative orders of the commutation parameters. Consequently, \(A\) satisfies the...