Periodic modules over general quantum Laurent polynomials
We preserve the notation of the preceding review Zbl 0924.16005. The author continues with investigation of finitely generated \(A\)-modules [initiated in Mat. Zametki 59, No. 4, 497-503 (1996; Zbl 0879.16013), Mat. Sb. 185, No. 7, 3-12 (1994; Zbl 0849.16003)]. The main result is: if \(M\) is a non-zero finitely generated periodic (i.e. torsion) \(A\)-module then \(M\) is cyclic and there exists a basis \(Y_1,\dots,Y_n\) of \(G\) such that \(M\) is finitely generated projective over the subalgebra generated by \(D\) and \(Y_1,\dots,Y_{n-1}\).
scientific article; zbMATH DE number 1237975