Decomposition of Jordan automorphisms of strictly triangular matrix algebra over local rings

✍ Scribed by Xing Tao Wang; Hong You

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 217 KB
• Volume: 392
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2004.06.009

✦ Synopsis

Let N n+1 (R) be the algebra of all strictly upper triangular n + 1 by n + 1 matrices over a 2-torsionfree commutative local ring R with identity. In this paper, we prove that any Jordan automorphism of N n+1 (R) can be uniquely written as a product of a graph automorphism, a diagonal automorphism, an inner automorphism and a central automorphism for n 3. In the cases n = 1, 2, we also give a decomposition for any Jordan automorphism of N n+1 (R) (1 n 2).