论文标题
固定的扭曲的广义Weyl代数的环
Fixed rings of twisted generalized Weyl algebras
论文作者
论文摘要
扭曲的广义Weyl代数（TGWAS）是一个大型代数家族，其中包括戒指理论和表示理论的几个代数，例如Weyl代数，$ U（\ Mathfrak {sl} _2 _2）$的原始商，以及多载体量化的Weyl Algebras。在这项工作中，我们研究了在对角线自动形态下TGWA的不变性。在某些条件下，我们能够证明通过这种自动形态的TGWA的固定环再次是TGWA。特别是，对于$ \ bbbk $ - finitistic tgwas type $（a_1）^n $和$ a_2 $都是如此。我们将此定理应用于研究固定环的特性，例如Noetherian的性质和简单性。当限制在固定环的作用时，我们还要查看TGWA的简单重量模块的行为。作为辅助结果，为了研究TGWAS张量产品的不变剂，我们证明了常规的，$ $ $ - 一致的TGWAS类在张量产品下关闭。
Twisted generalized Weyl algebras (TGWAs) are a large family of algebras that includes several algebras of interest for ring theory and representation theory, such as Weyl algebras, primitive quotients of $U(\mathfrak{sl}_2)$, and multiparameter quantized Weyl algebras. In this work, we study invariants of TGWAs under diagonal automorphisms. Under certain conditions, we are able to show that the fixed ring of a TGWA by such an automorphism is again a TGWA. In particular, this is true for $\Bbbk$-finitistic TGWAs of type $(A_1)^n$ and $A_2$. We apply this theorem to study properties of the fixed ring, such as the noetherian property and simplicity. We also look at the behavior of simple weight modules for TGWAs when restricted to the action of the fixed ring. As an auxiliary result, in order to study invariants of tensor products of TGWAs, we prove that the class of regular, $μ$-consistent TGWAs is closed under tensor products.
