Stable equivalence of selfinjective algebras of tilted type

被引：0
|
作者：
Andrzej Skowroński
Kunio Yamagata
机构：
[1] Faculty of Mathematics and Informatics,
[2] Nicholas Copernicus University,undefined
[3] Chopina 12/18,undefined
[4] PL- 87-100 Toruń,undefined
[5] Poland,undefined
[6] Department of Mathematics,undefined
[7] Tokyo University of Agriculture and Technology,undefined
[8] Fuchu,undefined
[9] Tokyo 183,undefined
[10] Japan,undefined
来源：
Archiv der Mathematik | 1998年 / 70卷
关键词：
Tilted Algebra; Dynkin Type; Nakayama Automorphism; Repetitive Algebra; Selfinjective Algebra;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A finite dimensional K-algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\it\Lambda $\end{document} is called selfinjective of tilted type if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\it\Lambda $\end{document} is a quotient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\widehat {B}/(\varphi \nu _{\hat {B}})$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\widehat {B}$\end{document} is the repetitive algebra of a tilted algebra B not of Dynkin type, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\nu _{\hat {B}}$\end{document} is the Nakayama automorphism of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\widehat {B}$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\varphi $\end{document} is a positive automorphism of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\widehat {B}$\end{document}. We prove that a selfinjective algebra A is stably equivalent to a selfinjective algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\it\Lambda $\end{document} of tilted type if and only if A is socle equivalent to a selfinjective algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\it\Lambda $\end{document} of tilted type.
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页码：341 / 350
页数：9
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