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arXiv · 2010.04128

All exact Borel subalgebras and all directed bocses are normal

Teresa Conde
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Abstract

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.

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Teresa Conde. 2021-03-29. All exact Borel subalgebras and all directed bocses are normal. https://doi.org/10.1016/j.jalgebra.2021.03.025

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