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On derivations of algebras with involution

✍ Scribed by Joso Vukman

Publisher: Akadmiai Kiad
Year: 2006
Tongue: English
Weight: 151 KB
Volume: 112
Category: Article
ISSN: 1588-2632
DOI: 10.1007/s10474-006-0071-3

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Let A be an absolute valued algebra with involution, in the sense of Urbanik [K. Urbanik, Absolute valued algebras with an involution, Fund. Math. 49 (1961) 247-258]. We prove that A is finite-dimensional if and only if the algebra obtained by symmetrizing the product of A is simple, if and only if

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## Abstract It is shown that derivations on LMC\*‐algebras are always continuous and generate a continuous one‐parameter group of automorphisms. The structure of the derivation and the automorphism group on LMC\*‐algebras is investigated.