In some noncommutative algebras there are elements which can be in terms of a distinguished generators (resembling matrix entries of a generic matrix) written by formulas analogous to the formula for the usual determinant.
In some cases they have special properties, for example being central (e.g. in the case of Yangian).
In the case of quantum linear groups, as the usual determinant is related to the exterior algebra, the corresponding quantum determinant is related to a quantum exterior algebra. In some cases, quantum determinants may be written as products of quasideterminants, similarly to the usual determinant.
Historically, quantum determinants first appeared in the works of Leningrad school of quantum integrable systems.
For RTT algebras:
Created on June 17, 2024 at 13:23:51. See the history of this page for a list of all contributions to it.