Enhancing Lie color algebras

被引：0

作者：

Price, Kenneth L. ^{[1
,2
]}

机构：

[1] Univ Wisconsin Oshkosh, Dept Mathemt, Oshkosh, WI USA

[2] Univ Wisconsin Oshkosh, Dept Mathemt, 800 Algoma Blvd, Oshkosh, WI 54901 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 05期

关键词：

Lie color algebra; universal enveloping algebra; ENVELOPING-ALGEBRAS; PRIMENESS; CRITERION;

D O I：

10.1080/00927872.2023.2278667

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Lie color algebras generalize Lie superalgebras. We adapt a construction of Bahturin and Pagon to create enhanced Lie color algebras. This construction offers a much-needed method for constructing simple Lie color algebras. To illustrate its applicability, we demonstrate how to enhance any simple Lie superalgebra and obtain a simple Lie color algebra. Additionally, we show that if a Lie color algebra has a nonzero determinant, this property extends to its enhancement. This ensures its universal enveloping algebra is semiprime. Extra conditions on the grading group provide a primeness criterion.

引用

页码：1956 / 1964

页数：9

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