Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves
Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves
复制标题
量子矩阵、完全非负元胞和辛叶中的环面不变素理想
DOI：
10.1007/s00209-010-0714-5
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发表时间：
2009
影响因子：
0.8
通讯作者：
T. Lenagan
中科院分区：
文献类型：
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作者：
K. Goodearl;S. Launois;T. Lenagan
给定大小的量子矩阵的代数通过自同构支持一个有理环面作用。由莱茨特（Letzter）和第一作者的工作可知，要理解这个代数的素谱和本原谱，第一步是理解在环面作用下不变的素理想。在本文中，我们证明了一族量子子式是属于量子矩阵代数的一个给定的环面不变素理想的所有量子子式的集合，当且仅当相应的子式族在适当大小的完全非负实矩阵空间中定义了一个非空的完全非负胞腔。作为一个推论，在量子化参数\(q\)在\({\mathbb{Q}}\)上是超越的情况下，我们得到了量子矩阵的环面不变素理想的量子子式的显式生成集。
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 $${\mathbb{Q}}$$.
量子格拉斯曼的素理想
DOI：
10.1007/s00029-008-0054-z
发表时间：
2008
期刊：
Selecta Mathematica
影响因子：
--
作者：
Launois S
通讯作者：
Launois S