A Self-injective Cellular Algebra Is Weakly Symmetric☆
A Self-injective Cellular Algebra Is Weakly Symmetric☆
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DOI：
10.1006/jabr.1999.8037
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发表时间：
2000-06
影响因子：
0.9
通讯作者：
Steffen König;Changchang Xi
中科院分区：
文献类型：
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作者：
Steffen König;Changchang Xi
这里自射意味着每个射影模块也是单射的，而弱对称则表示任何给定简单模块的射影覆盖是同一简单模块的射影包络。也就是说，排列 top(P ) 7→ soc(P ) （对于 P 不可分解的射影-内射）是恒等式。众所周知，一般来说，所有这些包含在内都是正确的。这篇笔记的主要结果表明，在细胞代数类（包含对称群的群代数、各种 Hecke 代数、Brauer 代数、Temperley-Lieb 代数，...，参见 [2]）内，这些包含物中的第三个是恒等式。
Here self–injective means that each projective module is injective as well, whereas weakly symmetric says that the projective cover of any given simple module is the injective envelope of the same simple module. That is, the permutation top(P ) 7→ soc(P ) (for P indecomposable projective–injective) is the identity. It is well–known that in general all these inclusions are proper. The main result of this note states that inside the class of cellular algebras (which contains group algebras of symmetric groups, various kinds of Hecke algebras, Brauer algebras, Temperley–Lieb algebras, ..., see [2]) the third one of these inclusions is an identity.