Mutations of C*-algebras and quasiassociative JB*-algebras

• Autores: Ángel Rodríguez Palacios
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 38, Fasc. 2, 1987, págs. 131-135
• Idioma: inglés
• Títulos paralelos:
  • Mutaciones de C*-álgebras y JB*-álgebras cuasi-asociativas
• Enlaces
  • Texto completo
• Resumen

  • The centroid of an algebra $A$ is the largest ring over which $A$ can be regarded as an algebra. In case $A$ is a $C^\ast$-algebra, the centroid of $A$ also has a natural structure of $C^\ast$-algebra and, for $f$ in the centroid of $A$ with $0\leq f\leq 1$, the $f$-mutation of $A$ (denoted $A^{(f)}$) with the same norm as $A$ is a (complete) normed algebra in the classical sense that the norm is submultiplicative (see [4], section 2). To be more precise, the algebras $A^{(f)}$ as above are examples of noncommutative $JB^\ast$-algebras (see [2] for definition) which are split quasiassociative over their centroids. In this note we prove that there are no other examples, thus answering by the desired negative a problem posed in [4]. Our proof is strongly based in the main result in [4] and the Dauns-Hofmann theorem.