Dimension and enumeration of primitive ideals in quantum algebras
Dimension and enumeration of primitive ideals in quantum algebras
复制标题
量子代数中本原理想的维数和枚举
DOI：
10.1007/s10801-008-0132-5
复制
发表时间：
2007
影响因子：
0.8
通讯作者：
N. Nguyen
中科院分区：
文献类型：
--
作者：
J. Bell;S. Launois;N. Nguyen
在本文中，我们研究了支持有理环面作用的量子代数的原始理想。我们首先证明迪克斯米尔定理的量子模拟；也就是说，我们证明了各种量子代数的本原因子的 Gelfand-Kirillov 维数总是偶数。接下来，我们给出在环面作用下不变的素理想的组合准则，使其成为本原。我们使用这个准则来获得在环面作用下不变的 2×n 量子矩阵代数中本原理想数的公式。粗略地说，这可以被认为是给出“各种 2×n 量子矩阵”中在环面诱导作用下不变的点的枚举。
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 2×n 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 2×n quantum matrices”.