Classification of arithmetic root systems
Classification of arithmetic root systems
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DOI：
10.1016/j.aim.2008.08.005
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发表时间：
2006-05
影响因子：
1.7
通讯作者：
I. Heckenberger
中科院分区：
文献类型：
--
作者：
I. Heckenberger
算术根系是对角型尼科尔斯代数的不变量，具有一定的有限性。它们也可以被认为是普通根系统的概括，具有丰富的结构和许多新的例子。另一方面，尼科尔斯代数是构建量子化包络代数、量子群的非交换微分几何以及通过 Andruskiewitsch 和 Schneider 的提升方法对尖 Hopf 代数进行分类的基本对象。在本文中，算术根系统被完全概括地分类。作为副产品，获得了许多新的有限维点 Hopf 代数。
Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. They can also be considered as generalizations of ordinary root systems with rich structure and many new examples. On the other hand, Nichols algebras are fundamental objects in the construction of quantized enveloping algebras, in the noncommutative differential geometry of quantum groups, and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. In the present paper arithmetic root systems are classified in full generality. As a byproduct many new finite dimensional pointed Hopf algebras are obtained.