caa a22 4500 397532881 CHVBK 20180308164656.0 cr unu---uuuuu 161202e199510 xx s 000 0 eng 10.1112/jlms/52.2.255 doi (NATIONALLICENCE)oxford-10.1112/jlms/52.2.255 Vancliff M. Department of Mathematics, University of Washington Seattle, Washington 98195, USA The Defining Relations of Quantum n × n Matrices [Elektronische Daten] [M. Vancliff] Let 𝒪q(Mn) denote the coordinate ring of quantum n × n matrices. We show there exists a subvariety 𝒫n of P(Mn) and an automorphism σn of 𝒫n such that 𝒪q(Mn) determines, and is determined by, the geometric data {𝒫n, σn}; the linear span of the defining relations of 𝒪q(Mn) is the set of all those elements of Mn* ⊗ Mn* that vanish on the graph of σn. Moreover, if q2 ≠ 1, the variety 𝒫n is independent of q. Our main result is that there are two natural descriptions of 𝒫n. Firstly, if q ∈ k×, there is a natural bijection between 𝒫n and the point modules over 𝒪q(Mn), and the automorphism σn is the shift functor on point modules. Secondly, since 𝒪q(Mn) is a graded flat deformation of 𝒪1(Mn) the polynomial ring 𝒪(Mn), there is a homogeneous Poisson bracket on 𝒪(Mn) and an associated Poisson structure on P(Mn). In this context, if q2 ≠ 1, the variety 𝒫n consists of those points of P(Mn) which are the zero-dimensional symplectic leaves with respect to this Poisson structure. © The London Mathematical Society Notes and Papers nationallicence Journal of the London Mathematical Society Oxford University Press 52/2(1995-10), 255-262 0024-6107 52:2<255 1995 52 jlms https://doi.org/10.1112/jlms/52.2.255 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1112/jlms/52.2.255 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vancliff M. Department of Mathematics, University of Washington Seattle, Washington 98195, USA NATIONALLICENCE 773 0- Journal of the London Mathematical Society Oxford University Press 52/2(1995-10), 255-262 0024-6107 52:2<255 1995 52 jlms Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford