1. Loewy coincident algebra and $QF$-3 associated graded algebra
- Creator:
- Tachikawa, Hiroyuki
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- associated graded algebra, $QF$ algebra, $QF$-3 algebra, upper Loewy series, and lower Loewy series
- Language:
- English
- Description:
- We prove that an associated graded algebra $R_G$ of a finite dimensional algebra $R$ is $QF$ (= selfinjective) if and only if $R$ is $QF$ and Loewy coincident. Here $R$ is said to be Loewy coincident if, for every primitive idempotent $e$, the upper Loewy series and the lower Loewy series of $Re$ and $eR$ coincide. \endgraf $QF$-3 algebras are an important generalization of $QF$ algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra $R$, the associated graded algebra $R_G$ is $QF$-3 if and only if $R$ is $QF$-3.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public