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

Fingerprint

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

Liau, P. K., & Liu, C-K. (2014). Invariants of algebraic derivations and automorphisms in Banach algebras. Journal of Algebra, 403, 313-323. https://doi.org/10.1016/j.jalgebra.2013.10.035

@article{5398b10985164eb7a1e8db5152eee4d2,

title = "Invariants of algebraic derivations and automorphisms in Banach algebras",

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.",

author = "Liau, {Pao Kuei} and Cheng-Kai Liu",

year = "2014",

month = feb

day = "1",

doi = "10.1016/j.jalgebra.2013.10.035",

language = "English",

volume = "403",

pages = "313--323",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Invariants of algebraic derivations and automorphisms in Banach algebras

AU - Liau, Pao Kuei

AU - Liu, Cheng-Kai

PY - 2014/2/1

Y1 - 2014/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84893426015&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893426015&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2013.10.035

DO - 10.1016/j.jalgebra.2013.10.035

M3 - Article

AN - SCOPUS:84893426015

VL - 403

SP - 313

EP - 323

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

Access to Document

10.1016/j.jalgebra.2013.10.035