On strongly quasi-hereditary algebras

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.

This manuscript has been withdrawn by the author. All the results are included in the article arXiv:1705.03279 by the author

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• Rejective subcategories of artin algebras and orders
• From Submodule Categories to the Stable Auslander Algebra
• The Ringel dual of the Auslander-Dlab-Ringel algebra