Goodearl, Ken and Launois, S. and Lenagan, T.H.
(2011)
*Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves.*
Mathematische Zeitschrift, 269
(1).
pp. 29-45.
ISSN 0025-5874.
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Official URL http://dx.doi.org/10.1007/s00209-010-0714-5 |

## Abstract

The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step is to understand the prime ideals that are invariant under the torus action. In this paper, we prove that a family of quantum minors is the set of all quantum minors that belong to a given torus-invariant prime ideal of a quantum matrix algebra if and only if the corresponding family of minors defines a non-empty totally nonnegative cell in the space of totally nonnegative real matrices of the appropriate size. As a corollary, we obtain explicit generating sets of quantum minors for the torus-invariant prime ideals of quantum matrices in the case where the quantisation parameter q is transcendental over Q.

Item Type: | Article |
---|---|

Subjects: | Q Science > QA Mathematics (inc Computing science) Q Science > QA Mathematics (inc Computing science) > QA150 Algebra |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |

Depositing User: | Stephane Launois |

Date Deposited: | 19 Sep 2011 14:49 |

Last Modified: | 11 Nov 2011 11:47 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/28177 (The current URI for this page, for reference purposes) |

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