Bell, Jason and Launois, Stephane and Nguyen, N.
(2009)
*Dimension and enumeration of primitive ideals in quantum algebras.*
Journal of Algebraic Combinatorics, 29
(3).
pp. 269-294.
ISSN 0925-9899 .
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Official URL http://dx.doi.org/10.1007/s10801-008-0132-5 |

## Abstract

In this paper, we study the primitive ideals of quantum algebras supporting a rational torus action. We first prove a quantum analogue of a Theorem of Dixmier; namely, we show that the Gelfand-Kirillov dimension of primitive factors of various quantum algebras is always even. Next we give a combinatorial criterion for a prime ideal that is invariant under the torus action to be primitive. We use this criterion to obtain a formula for the number of primitive ideals in the algebra of 2xn quantum matrices that are invariant under the action of the torus. Roughly speaking, this can be thought of as giving an enumeration of the points that are invariant under the induced action of the torus in the "variety of 2xn quantum matrices".

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

Uncontrolled keywords: | Primitive ideals; Quantum matrices; Quantised enveloping algebras; Cauchon diagrams; Perfect matchings; Pfaffians |

Subjects: | Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics |

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

Depositing User: | Stephane Launois |

Date Deposited: | 25 Sep 2009 08:01 |

Last Modified: | 28 May 2014 10:55 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/17523 (The current URI for this page, for reference purposes) |

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