Vladislav Khartchenko

The Koszul algebras arise in many areas of the modern mathematics: algebraic geometry, representation theory, noncommutative geometry, topology, number theory, theory of pseudoroots of noncommutative polynomials. 

We prove that in q-Weyl generators the multi-parameter Drinfeld-Jimbo quantizations of type A_n^+ and B_n^+ are quadratic-linear Koszul algebras. 

At the same time, the quantization of type G_2^+ is a quadratic-linear algebra but not a quadratic-linear Koszul algebra.