Özkay ÖZKAN, Mustafa AKKURT

95111

Automorphisms of a certain subalgebra of the upper triangular matrix algebra

For a commutative ring $R$ with unity, the $R$-algebra of strictly upper triangular $n\times n$ matrices over $R$ is denoted by $N_{n}\left( R\right) $, where $n$ is a positive integer greater than $1$. For the identity matrix $I$, $\alpha \in R$, $A \in N_n(R)$, the set of all elements $\alpha I+A$ is defined as the scalar upper triangular matrix algebra $ST_n(R)$ which is a subalgebra of the upper triangular matrices $T_n(R) .$ In this paper, we investigate the $R$-algebra automorphisms of $ST_{n}\left( R\right) .$ We extend the automorphisms of $N_{n}\left( R\right) $ to $ST_{n}\left( R\right)$ and classify all the automorphisms of $ST_{n}\left( R\right) .$ We generalize the results of Cao and Wang and prove that not all automorphisms of $ST_{n}\left( R\right) $ can be extended to the automorphisms of $T_{n}(R).$
Keywords:

triangular matrix algebra upper triangular matrix algebra, automorphisms,

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  • [1] Y. Cao and J. Wang, A note on algebra automorphisms of strictly upper triangular matrices over commutative rings, Linear Algebra Appl. 311, 187–193, 2000.
  • [2] S.P. Coelho, Automorphism group of certain algebras of triangular matrices, Arch. Math. 61, 119–123, 1993.
  • [3] T.P. Kezlan, A note on algebra automorphisms of triangular matrices over commutative rings, Linear Algebra Appl. 135, 181–184, 1990.
Hacettepe Journal of Mathematics and Statistics-Cover
  • Yayın Aralığı: 6
  • Başlangıç: 2002
  • Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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