Mixed standardization and Ringel duality
Takahide Adachi, Mayu Tsukamoto
TL;DR
This paper introduces mixed stratified algebras, generalizing standardly stratified algebras using Dlab--Ringel's standardization, and explores their Ringel duality through stratifying systems.
Contribution
It constructs mixed stratified algebras via Dlab--Ringel's method and investigates their Ringel duality, extending the theory of stratified algebras.
Findings
Introduction of mixed stratified algebras
Establishment of their Ringel duality properties
Extension of stratification theory
Abstract
Dlab--Ringel's standardization method gives a realization of a standardly stratified algebra. In this paper, we construct mixed stratified algebras, which are a generalization of standardly stratified algebras, following Dlab--Ringel's standardization method. Moreover, we study a Ringel duality of mixed stratified algebras from the viewpoint of stratifying systems.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Rings, Modules, and Algebras