Presenting degenerate Ringel-Hall algebras of type B

被引：4

作者：

Fan LiJuan ^{[2
]}

Zhao ZhongHua ^{[1
]}

机构：

[1] Beijing Univ Chem Technol, Sch Sci, Dept Math & Comp Sci, Beijing 100029, Peoples R China

[2] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2012年 / 55卷 / 05期

关键词：

degenerate Ringel-Hall algebras; generic extension monoid algebras; Auslander-Reiten quivers; Frobenius morphism; FINITE; EXTENSIONS; MODULES; BASES;

D O I：

10.1007/s11425-011-4317-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a presentation for the degenerate Ringel-Hall algebras of type B by studying the corresponding generic extension monoid algebras. As an application, it is shown that the degenerate Ringel-Hall algebras of type B admit multiplicative bases.

引用

页码：949 / 960

页数：12

共 17 条

[1] On degenerations and extensions of finite dimensional modules [J].

Bongartz, K .

ADVANCES IN MATHEMATICS, 1996, 121 (02) :245-287

[2]

Deng B, 2008, MATH SURVEYS MONOGRA, V759

[3] Generic extensions and canonical bases for cyclic quivers [J].

Deng, Bangming ;

Du, Jie ;

Xiao, Jie .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2007, 59 (06) :1260-1283

[4] Frobenius morphisms and representations of algebras [J].

Deng, Bangming ;

Du, Jie .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (08) :3591-3622

[5] Presenting degenerate Ringel-Hall algebras of cyclic quivers [J].

Deng, Bangming ;

Du, Jie ;

Mah, Alexandre .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2010, 214 (10) :1787-1799

[6] ALGEBRAS OF FINITE REPRESENTATION TYPE [J].

DLAB, V ;

RINGEL, CM .

JOURNAL OF ALGEBRA, 1975, 33 (02) :306-394

[7]

DLAB V, 1976, MEMOIRS AM MATH SOC, V6

[8]

MAH A, 2006, THESIS U NEW S WALES

[9] Feigin's map and monomial bases for quantized enveloping algebras [J].

Reineke, M .

MATHEMATISCHE ZEITSCHRIFT, 2001, 237 (03) :639-667

[10]

Reineke M, ARXIVMATH0206095V1

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