On the Braid Group Action on Exceptional Sequences for Weighted Projective Lines

IF 0.5 4区 数学 Q3 MATHEMATICS Algebras and Representation Theory Pub Date : 2023-11-23 DOI:10.1007/s10468-023-10243-9
Edson Ribeiro Alvares, Eduardo Nascimento Marcos, Hagen Meltzer
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Abstract

We give a new and intrinsic proof of the transitivity of the braid group action on the set of full exceptional sequences of coherent sheaves on a weighted projective line. We do not use the corresponding result of Crawley-Boevey for modules over hereditary algebras. As an application we prove that the strongest global dimension of the category of coherent sheaves on a weighted projective line \(\mathbb {X}\) does not depend on the parameters of \(\mathbb {X}\). Finally we prove that the determinant of the matrix obtained by taking the values of n \(\mathbb {Z}\)-linear functions defined on the Grothendieck group \(\textrm{K}_0(\mathbb {X}) \simeq \mathbb {Z}^n \) of the elements of a full exceptional sequence is an invariant, up to sign.

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加权投影线例外序列上的辫群作用
给出了加权投影线上相干束的满例外序列集上辫群作用可传递性的一个新的内在证明。对于遗传代数上的模,我们没有使用Crawley-Boevey的相应结果。作为一个应用,我们证明了在加权投影线\(\mathbb {X}\)上相干轴类的最强整体维数不依赖于\(\mathbb {X}\)的参数。最后证明了在一个满例外序列的元素的Grothendieck群\(\textrm{K}_0(\mathbb {X}) \simeq \mathbb {Z}^n \)上定义的n个\(\mathbb {Z}\) -线性函数的值所得到的矩阵的行列式是不变的,直到符号。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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