论文标题
准laurent多项式代数的自动形态和表示
Automorphisms and representations of quasi Laurent polynomial algebras
论文作者
论文摘要
我们研究了准多项式代数（QPA）和准laurent多项式代数（QLPA）的自动形态和表示。对于由任意偏斜的对称积分矩阵定义的任何QLPA，我们以通用$ Q $和Unity的根源明确描述其自动形态组。任何QLPA均与$ Q $的不同权力和中心的QLPA副本的张量相同，因此QPA和QLPA的表示大大减少了$ {\ Mathcal L} _Q（2）$ and $ {\ n e} $ Q. $ 2 $。我们研究了$ {\ Mathcal a} _q（2）$ - 模块的类别，这些模块具有具有自然局部有限属性的子模块有限覆盖物，并满足了本地化下的某些条件，确定其块，对简单对象进行分类并为Simplace提供两个明确的构造。一种结构产生简单的$ {\ Mathcal a} _q（2）$ - 来自$ {\ Mathcal l} _q（2）$ - 通过单态模块的模块，该模块由$ {\ Mathcal a} _q（2）$ in $ {\ MATHCAL l} $的自然嵌入$ {\ Mathcal a} _q（2） $ {\ MATHCAL L} _Q（2）$，另一个探讨了algebra $ {\ Mathcal d} _Q $ {\ Mathcal d} _Q $ $ q $ $ q $ -divferential operators for Algebra $ {\ Mathcal d} _Q $的类别。
We study automorphisms and representations of quasi polynomial algebras (QPAs) and quasi Laurent polynomial algebras (QLPAs). For any QLPA defined by an arbitrary skew symmetric integral matrix, we explicitly describe its automorphism groups at generic $q$ and at roots of unity. Any QLPA is isomorphic to the tensor product of copies of the QLPA of degree $2$ at different powers of $q$ and the centre, thus the study of representations of QPAs and QLPAs largely reduces to that of ${\mathcal L}_q(2)$ and ${\mathcal A}_q(2)$, the QLPA and QPA of degree $2$. We study a category of ${\mathcal A}_q(2)$-modules which have finite covers by submodules with natural local finiteness properties and satisfy some condition under localisation, determining its blocks, classifying the simple objects and providing two explicitly constructions for the simples. One construction produces the simple ${\mathcal A}_q(2)$-modules from ${\mathcal L}_q(2)$-modules via monomorphisms composed of the natural embedding of ${\mathcal A}_q(2)$ in ${\mathcal L}_q(2)$ and automorphisms of ${\mathcal L}_q(2)$, and the other explores a class of holonomic ${\mathcal D}_q$-modules for the algebra ${\mathcal D}_q$ of $q$-differential operators.
