Matrix-element bialgebras determined by quadratic coordinate algebras
Some properties of nonstandard quantum deformations of \(GL(n)\) are difficult to establish or require very lengthy calculations. If the nonstandard deformation is related to a standard one via a twisting operation one can reduce the problem to the case of one-parameter deformations. In this paper the author provides a more systematic approach to general quantum deformations which promises to facilitate the establishing of certain properties of these Hopf algebras, such as polynomiality or the existence of the antipode. The method is based on a construction of Manin. The author uses this method in certain special cases such as the \(N\)-parameter deformation of \(GL(n)\) and some quantum groups arising from two-dimensional coordinate algebras.
\(N\)-parameter deformation of \(GL(n)\)
scientific article; zbMATH DE number 480477