Unipotent Radicals of the Standard Borel and Parabolic Subgroups in Quantum Special Linear Groups
Unipotent Radicals of the Standard Borel and Parabolic Subgroups in Quantum Special Linear Groups
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量子特殊线性群中标准Borel和抛物线子群的单能根
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发表时间：
2014
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通讯作者：
Andrew Jaramillo
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作者：
Andrew Jaramillo
作者：安德鲁·塞西尔·哈拉米洛 |顾问：Goodearl, Kenneth |摘要: 在本文中，我们发现了量子特殊线性群中标准Borel和标准抛物线子群的单能基的坐标环的非交换类似物。在每种情况下，定义了两个子代数，这两个子代数都可以被视为标准 Borel 或标准抛物线子群的单能根的量化。对这些代数进行了演示。还表明，这些代数是作为从量子特殊线性群上的 Hopf 代数结构导出的自然余模代数作用的共变子代数而出现的。
Author(s): Jaramillo, Andrew Cecil | Advisor(s): Goodearl, Kenneth | Abstract: In this dissertation we find noncommutative analogues of the coordinate rings of the unipotent radicals of the standard Borel and standard parabolic subgroups in quantum special linear groups. In each case, two subalgebras are defined, both of which can be considered quantizations of the unipotent radical of a standard Borel or a standard parabolic subgroup. Presentations are given for these algebras. It is also shown that these algebras arise as a coinvariant subalgebra of a natural comodule algebra action induced from the Hopf algebra structure on quantum special linear groups.