Simple Jordan Color Algebras Arising from Associative Graded Algebras

✍ Scribed by Jeffrey Bergen; Piotr Grzeszczuk

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 220 KB
• Volume: 246
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.9005

✦ Synopsis

If R is a G-graded associative algebra, where G is an abelian group and ⑀ is a bicharacter for G, then R also has the structure of a Jordan color algebra. In addition, if R is endowed with a color involution ), then the symmetric elements S under ) are also a Jordan color algebra. Generalizing results of I. N. Herstein, we examine the Jordan color structure of R and S. In particular, we show that if R is a graded-simple algebra, then both R and S are simple Jordan color algebras, except for some special cases which cannot arise in the ordinary case.