Quantum determinants and quasideterminants

Abstract

Quasideterminants and quasiminors of a matrix with notnecessarily commuting entries were introduced by I. M. Gel fandand V. S. Retakh [see, e.g., Funktsional. Anal. i Prilozhen. 26(1992), no. 4, 1 20, 96; MR 94b:15003]. Many well knownnoncommutative determinants such as the Berezinian and variousdeterminants arising in the theory of quantum groups can beexpressed as products of commuting quasiminors.\par The aim ofthis paper is to extend this result to a class of Hopf algebrasintroduced by Faddeev, Reshetikhin and Takhtajan, where the Rmatrix is deformed by an upper triangular twist.\par The lastsection of the paper discusses a construction of upper triangulartwists due to Hodges