论文标题
所有精确的Borel子代理和所有定向Bocses均正常
All exact Borel subalgebras and all directed bocses are normal
论文作者
论文摘要
最近，Brzeziński，Koenig和Külshammer引入了准植虫式代数的正常精确Borel subgerbra的概念。他们已经表明，正常的定向Bocses和Quasiherepitary代数之间存在正常且同源精确的Borel亚词法之间的一对一对应关系。在此简短说明中，我们证明每个确切的Borel子代理都会自动正常。作为推论，我们得出的结论是，每个定向的BOC都有类似组的元素。这些结果简化了Brzeziński，Koenig和Külshammer的培养。
Recently, Brzeziński, Koenig and Külshammer have introduced the notion of normal exact Borel subalgebra of a quasihereditary algebra. They have shown that there exists a one-to-one correspondence between normal directed bocses and quasihereditary algebras with a normal and homological exact Borel subalgebra. In this short note, we prove that every exact Borel subalgebra is automatically normal. As a corollary, we conclude that every directed bocs has a group-like element. These results simplify Brzeziński, Koenig and Külshammer's bijection.
