Introducing crystalline graded algebras. (Q2478184)

Let \(A=\bigoplus_{g\in G}A_g\) be an associative algebra with a unit element graded by a group \(G\). It is assumed that each \(A_g\) is a free cyclic (left and right) \(A_0\)-module with a normal free generator. Then we get a 2-cocycle in \(A_0\) generating a multiplicative subset in \(A_0\). The authors consider the case when \(A_0\) is \(S(G)\)-torsion-free and when \(S(G)\) is an Ore set in \(A_0\). It is shown that quantum Weyl algebras, generalized Weyl algebras, can be obtained in this way.