Groups of Extended Affine Lie Type

被引：3

作者：

Azam, Saeid ^{[1
,2
]}

Farahmand Parsa, Amir ^{[2
]}

机构：

[1] Univ Isfahan, Dept Math, POB 81745-163, Esfahan, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 2019年 / 55卷 / 03期

关键词：

Extended affine; Steinberg; Kac-Moody; WEYL GROUPS; ALGEBRAS;

D O I：

10.4171/PRIMS/55-3-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie algebra. Afterwards, we show that the extended affine Weyl group of the ground Lie algebra can be recovered as a quotient group of two subgroups of the group associated to the underlying algebra similar to Kac-Moody groups.

引用

页码：627 / 649

页数：23

共 24 条

[1] Covering algebras I. Extended affine Lie algebras [J].

Allison, B ;

Berman, S ;

Pianzola, A .

JOURNAL OF ALGEBRA, 2002, 250 (02) :485-516

[2]

Allison B. N., 1997, MEM AM MATH SOC, V126

[3] A characterization of affine Kac-Moody lie algebras [J].

Allison, BN ;

Berman, S ;

Gao, Y ;

Pianzola, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 185 (03) :671-688

[4]

[Anonymous], LECT CHEVALLEY GROUP

[5]

[Anonymous], 2001, Selecta Mathematica

[6] On the relation of extended affine Weyl groups and indefinite Weyl groups [J].

Azam, S .

JOURNAL OF ALGEBRA, 1999, 222 (01) :174-189

[7] Extended affine Weyl groups [J].

Azam, S .

JOURNAL OF ALGEBRA, 1999, 214 (02) :571-624

[8] A presentation for reduced extended affine Weyl groups [J].

Azam, S .

COMMUNICATIONS IN ALGEBRA, 2000, 28 (01) :465-488

[9] j Jordan tori for a torsion free abelian group [J].

Azam, Saeid ;

Yoshii, Yoji ;

Yousofzadeh, Malihe .

FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (03) :477-509

[10] EXTENDED AFFINE WEYL GROUPS: PRESENTATION BY CONJUGATION VIA INTEGRAL COLLECTION [J].

Azam, Saeid ;

Shahsanaei, Valiollah .

COMMUNICATIONS IN ALGEBRA, 2011, 39 (02) :730-749

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