The automorphism group of the quantum grassmannian
The automorphism group of the quantum grassmannian
复制标题
DOI：
10.1112/blms.12994
复制
发表时间：
2023-01
影响因子：
0.9
通讯作者：
S. Launois;T. Lenagan
中科院分区：
文献类型：
--
作者：
S. Launois;T. Lenagan
量子化坐标代数的自同构群通常比经典坐标代数的自同构群小得多。然而，这些自同构群往往很难计算。在本文中，我们计算了形变参数不是单位根的情况下量子格子的自同构群。所用的主要工具是反齐次化方程，它表明量子格罗曼的定域化等于量子矩阵的斜洛朗扩张。这个等式被用来连接量子矩阵的自同构群和量子矩阵的自同构群，其中自同构群是已知的。
The automorphism group of a quantised coordinate algebra is usually much smaller than that of its classical counterpart. Nevertheless, these automorphism groups are often very difficult to calculate. In this paper, we calculate the automorphism group of the quantum grassmannian in the case that the deformation parameter is not a root of unity. The main tool employed is the dehomogenisation equality which shows that a localisation of the quantum grassmannian is equal to a skew Laurent extension of quantum matrices. This equality is used to connect the automorphism group of the quantum grassmannian with that of quantum matrices, where the automorphism group is known.