ON MATRIX WREATH PRODUCTS OF ALGEBRAS

被引：5

作者：

Alahmadi, Adel ^{[1
]}

Alsulami, Hamed ^{[1
]}

Jain, S. K. ^{[2
]}

Zelmanov, Efim ^{[3
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Jeddah, Saudi Arabia

[2] Ohio Univ, Dept Math, Athens, OH 45701 USA

[3] Univ Calif San Diego, Dept Math, San Diego, CA 92103 USA

来源：

ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES | 2017年 / 24卷

基金：

美国国家科学基金会;

关键词：

growth function; associative algebra; wreath product; GELFAND-KIRILLOV DIMENSION; POLYNOMIALLY BOUNDED GROWTH; NIL ALGEBRAS; LIE-ALGEBRAS;

D O I：

10.3934/era.2017.24.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new construction of matrix wreath products of algebras that is similar to the construction of wreath products of groups introduced by L. Kaloujnine and M. Krasner [17]. We then illustrate its usefulness by proving embedding theorems into finitely generated algebras and constructing nil algebras with prescribed Gelfand-Kirillov dimension.

引用

页码：78 / 86

页数：9

共 30 条

[11] GELFAND-KIRILLOV DIMENSION
BORHO, W
KRAFT, H
[J]. MATHEMATISCHE ANNALEN, 1976, 220 (01) : 1 - 24
[12] Prime and primitive algebras with prescribed growth types
Greenfeld, Be'eri
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2017, 220 (01) : 161 - 174
[13] Grigorchuk R.I., 1984, IZV AKAD NAUK SSSR, V48, P939
[14] Higman B. H., 1949, Jour-nal of the London Mathematical Societys1-24, P247, DOI 10.1112/jlms/s1-24.4.247
[15] KALOUJNINE L, 1948, CR HEBD ACAD SCI, V227, P806
[16] PROBLEMS IN THEORY OF RINGS REVISITED
KAPLANSK.I
[J]. AMERICAN MATHEMATICAL MONTHLY, 1970, 77 (05) : 445 - &
[17] An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
Lenagan, T. H.
Smoktunowicz, Agata
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (04) : 989 - 1001
[18] NIL ALGEBRAS WITH RESTRICTED GROWTH
Lenagan, T. H.
Smoktunowicz, Agata
Young, Alexander A.
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2012, 55 : 461 - 475
[19] Malcev A, 1952, USPEKHI MAT NAUK, V7, P181
[20] A QUASI-ISOMETRIC EMBEDDING THEOREM FOR GROUPS
Olshanskii, Alexander Yu
Osin, Denis V.
[J]. DUKE MATHEMATICAL JOURNAL, 2013, 162 (09) : 1621 - 1648

← 1 2 3 →