论文标题
temperley-lieb代数和相对优势维度
Quasi-hereditary covers of Temperley-Lieb algebras and relative dominant dimension
论文作者
论文摘要
表示理论中的许多连接和二元性可以使用rouquier的质量封面来解释。姓名作者最近引入的相对主导和共同维度相对主导和共同维度的概念是评估和分类准纯粹的覆盖物的重要工具。 在本文中，我们证明，与特征倾斜模块的总和$ q $相对于特征倾斜模块的汇总$ q $，具有简单的二元性的常规模块的相对主导尺寸等于特征倾斜模块的相对优势维度的两倍，而不是$ q $。 To resolve the Temperley-Lieb algebras of infinite global dimension, we apply this result to the class of Schur algebras $S(2, d)$ and $Q=V^{\otimes d}$ the $d$-tensor power of the 2-dimensional module and we completely determine the relative dominant dimension of the Schur algebra $S(2, d)$ with respect to $V^{\otimes D} $。这些结果的$ Q $ - 动物也将获得。 作为副产品，我们获得了连接$ q $ -schur代数和tembleley-lieb代数的林格式双二元组的Hemmer-Nakano型结果。从Temperley-Lieb代数的角度来看，我们获得了他们与$ Q $ -schur代数的Ringel Duals形成的与他们的准雌性封面的连接的第一个完整分类。 这些结果与积分设置兼容，我们使用它们来推断出$ q $ -schur代数的林格尔双重二元在整数上覆盖了laurent多项式在整数上，以及一些投影模块，是最佳的Quasi-hersedalendital封面。
Many connections and dualities in representation theory can be explained using quasi-hereditary covers in the sense of Rouquier. The concepts of relative dominant and codominant dimension with respect to a module, introduced recently by the first-named author, are important tools to evaluate and classify quasi-hereditary covers. In this paper, we prove that the relative dominant dimension of the regular module of a quasi-hereditary algebra with a simple preserving duality with respect to a summand $Q$ of a characteristic tilting module equals twice the relative dominant dimension of a characteristic tilting module with respect to $Q$. To resolve the Temperley-Lieb algebras of infinite global dimension, we apply this result to the class of Schur algebras $S(2, d)$ and $Q=V^{\otimes d}$ the $d$-tensor power of the 2-dimensional module and we completely determine the relative dominant dimension of the Schur algebra $S(2, d)$ with respect to $V^{\otimes d}$. The $q$-analogues of these results are also obtained. As a byproduct, we obtain a Hemmer-Nakano type result connecting the Ringel duals of $q$-Schur algebras and Temperley-Lieb algebras. From the point of view of Temperley-Lieb algebras, we obtain the first complete classification of their connection to their quasi-hereditary covers formed by Ringel duals of $q$-Schur algebras. These results are compatible with the integral setup, and we use them to deduce that the Ringel dual of a $q$-Schur algebra over the ring of Laurent polynomials over the integers together with some projective module is the best quasi-hereditary cover of the integral Temperley-Lieb algebra.
