Invariants of algebraic derivations and automorphisms in Banach algebras

Pao Kuei Liau; Cheng-Kai Liu

doi:10.1016/j.jalgebra.2013.10.035

Invariants of algebraic derivations and automorphisms in Banach algebras

Pao Kuei Liau, Cheng-Kai Liu

Department of Mathematics

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We prove that if a semisimple real or complex Banach algebra A possesses an algebraic derivation whose invariants are algebraic, then A is finite-dimensional. This result is a full generalization of a recent result by Haily, Kaidi and Palacios (2011) [15] for the case of inner derivations in complex semisimple Banach algebras. The analogous result for automorphism case is also obtained.

Original language	English
Pages (from-to)	313-323
Number of pages	11
Journal	Journal of Algebra
Volume	403
DOIs	https://doi.org/10.1016/j.jalgebra.2013.10.035
Publication status	Published - 2014 Feb 1

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2013.10.035

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abstract = "We prove that if a semisimple real or complex Banach algebra A possesses an algebraic derivation whose invariants are algebraic, then A is finite-dimensional. This result is a full generalization of a recent result by Haily, Kaidi and Palacios (2011) [15] for the case of inner derivations in complex semisimple Banach algebras. The analogous result for automorphism case is also obtained.",

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