All exact Borel subalgebras and all directed bocses are normal

JOURNAL OF ALGEBRA

卷:579

Article

Conde, Teresa¹ 

[1] Univ Stuttgart, Inst Algebra & Number Theory, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Quasihereditary algebras;    Exact Borel subalgebras;    Bocses;   

DOI  :  10.1016/j.jalgebra.2021.03.025

来源: Elsevier

【 摘 要 】

Recently, Brzezinski, Koenig and Kulshammer have introduced the notion of normal exact Borel subalgebra of a quasi-hereditary 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 Brzezinski, Koenig and Kulshammer's bijection. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free