Quantum- and quasi-Plücker coordinates.
The paper is devoted to the study of non-commutative or quantum Grassmannians. The key tool is provided by the quasi-Plücker coordinates introduced as certain ratios of quasideterminants of \textit{I. M.\ Gelfand} and \textit{V. S.\ Retakh} [Sel. Math., New Ser. 3, 517--546 (1997; Zbl 0919.16011)]. In the commutative and quantum cases these specify to ratios of (quantum) minors. The main result of the paper is the reconstruction of the coordinate algebra of the quantum Grassmannian defined in [\textit{E.\ Taft} and \textit{J.\ Towber}, Algebra 142, 1--36 (1991; Zbl 0739.17007)] in terms of quasi-Plücker coordinates.
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