Cohomological stratification of diagram algebras
Cohomological stratification of diagram algebras
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图代数的上同调分层
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Rowena Paget
中科院分区：
文献类型：
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作者：
R. Hartmann;A. Henke;S. Koenig;Rowena Paget
细胞分层代数类被定义并显示为包括大类图代数。虽然定义是组合术语，但通过在 Graham 和 Lehrer 的细胞代数定义中添加额外的结构，可以根据精确函子和派生类别的分层建立各种结构属性。分层将“大”代数（例如布劳尔代数）与“较小”代数（例如对称群的群代数）联系起来。这些应用包括扩展 Hemmer 和 Nakano 以及 Hartmann 和 Paget 发现的类别的相对等价性，以及“大”和“小”代数的分解数和上同调群之间的恒等式。
The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural properties are established in terms of exact functors and stratifications of derived categories. The stratifications relate ‘large’ algebras such as Brauer algebras to ‘smaller’ ones such as group algebras of symmetric groups. Among the applications are relative equivalences of categories extending those found by Hemmer and Nakano and by Hartmann and Paget, as well as identities between decomposition numbers and cohomology groups of ‘large’ and ‘small’ algebras.