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arXiv · 1604.07606

On strongly quasi-hereditary algebras

Mayu Tsukamoto
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Abstract

Let $A$ be a finite dimensional algebra over an algebraically closed field $\mathbf{k}$. If $A$ is quasi-hereditary and the projective dimensions of all standard modules are at most one, then $A$ is called left strongly quasi-hereditary. In this paper, we construct a special heredity chain for left strongly quasi-hereditary algebras. Moreover, we show the quotient algebra by an ideal which appears in a special heredity chain of left strongly quasi-hereditary algebra is also left strongly quasi-hereditary algebra.

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Mayu Tsukamoto. 2016-04-26. On strongly quasi-hereditary algebras. https://arxiv.org/abs/1604.07606

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