Skew derivations with algebraic invariants of bounded degree

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• 作者：Jeffrey Bergen^a ; ¹ ; ^{jbergen@depaul.edu" class="auth_mail" title="E-mail the corresponding author} ; Piotr Grzeszczuk^b ; ² ; ^{piotrgr@pb.edu.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16N40 ; 16W25 ; 16W55 ; 47B47
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：447
• 期：Complete
• 页码：455-467
• 全文大小：315 K

文摘

This paper examines semiprime algebras A with a q-skew σ-derivation δ, where both δ and σ   are algebraic. With minor assumptions on the ground field, we show that if the invariants A^δ$A^{\delta }$ are algebraic of bounded degree, then A must be finite dimensional. As an application, it is shown that if A is a semiprime Banach algebra and δ   is continuous, then whenever A^δ$A^{\delta }$ is algebraic, it follows that A is finite dimensional.