MARTINDALE ALGEBRAS OF QUOTIENTS OF GRADED ALGEBRAS

被引：1

作者：

Bierwirth, H. ^{[1
]}

Martin Gonzalez, C. ^{[1
]}

Sanchez Ortega, J. ^{[2
]}

Siles Molina, M. ^{[1
]}

机构：

[1] Univ Malaga, Dept Algebra Geometria & Topol, E-29071 Malaga, Spain

[2] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

来源：

COMMUNICATIONS IN ALGEBRA | 2015年 / 43卷 / 02期

关键词：

Finitary; Graded algebra; Martindale ring of quotients; Maximal algebra of quotients; Strongly nondegenerate; SIMPLE LIE-ALGEBRAS; ASSOCIATIVE ALGEBRAS; GRADINGS;

D O I：

10.1080/00927872.2013.849266

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The motivation for this paper is the study of the relation between the zero component of the maximal graded algebra of quotients and the maximal graded algebra of quotients of the zero component, both in the Lie case and when considering Martindale algebras of quotients in the associative setting. We apply our results to prove that the finitary complex Lie algebras are (graded) strongly nondegenerate and compute their maximal algebras of quotients.

引用

页码：829 / 846

页数：18

共 18 条

[1] Finitary simple Lie algebras [J].

Baranov, AA .

JOURNAL OF ALGEBRA, 1999, 219 (01) :299-329

[2]

Beidar KI., 1996, Rings with Generalized Identities

[3] Lie ideals of graded associative algebras [J].

Bierwirth, Hannes ;

Siles Molina, Mercedes .

ISRAEL JOURNAL OF MATHEMATICS, 2012, 191 (01) :111-136

[4] Computing the maximal algebra of quotients of a Lie algebra [J].

Bresar, Matej ;

Perera, Francesc ;

Sanchez Ortega, Juana ;

Siles Molina, Mercedes .

FORUM MATHEMATICUM, 2009, 21 (04) :601-620

[5] Lie Quotients for Skew Lie Algebras [J].

Cabrera, Miguel ;

Sanchez Ortega, Juana .

ALGEBRA COLLOQUIUM, 2009, 16 (02) :267-274

[6] The socle of a nondegenerate Lie algebra [J].

Draper, Cristina ;

Lopez, Antonio Fernandez ;

Garcia, Esther ;

Lozano, Miguel Gomez .

JOURNAL OF ALGEBRA, 2008, 319 (06) :2372-2394

[7]

Gomez Lozano M., 2002, ACTA MATH HUNG, V97, P179

[8]

Lam T. Y., 1999, Lectures on modules and rings, DOI DOI 10.1017/CBO9780511546525

[9] Local rings of rings of quotients [J].

Lozano, M. A. Gomez ;

Molina, M. Siles .

ALGEBRAS AND REPRESENTATION THEORY, 2008, 11 (05) :425-436

[10] HERSTEIN LIE THEORY REVISITED [J].

MARTINDALE, WS ;

MIERS, CR .

JOURNAL OF ALGEBRA, 1986, 98 (01) :14-37

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