Absolute-valued algebras with an involution
K. Urbanik (1961)
Fundamenta Mathematicae
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K. Urbanik (1961)
Fundamenta Mathematicae
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K. Urbanik (1963)
Colloquium Mathematicum
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Rochdi, A. (2003)
International Journal of Mathematics and Mathematical Sciences
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B. Gleichgewicht (1963)
Colloquium Mathematicae
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José Antonio Cuenca Mira (1992)
Publicacions Matemàtiques
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In this note we introduce the concept of Cayley homomorphism which is closely related with those of composition algebra and normalized orthogonal multiplication. The key result shows the existence of certain types of Cayley homomorphisms for infinite dimension. As an application we prove the existence of left division infinite-dimensional complete normed real algebras with left unity.
Miguel Cabrera, José Martínez Aroza, Angel Rodríguez Palacios (1988)
Publicacions Matemàtiques
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We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution τ such that A = {b ∈ B : τ(b) = b*}. Using this, we obtain our main result, namely: (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically isomorphic.
Jerzy Płonka (1967)
Fundamenta Mathematicae
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H. Skala (1973)
Fundamenta Mathematicae
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Ana Rodríguez Palacios (1992)
Publicacions Matemàtiques
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We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation...
Seidon Alsaody (2011)
Colloquium Mathematicae
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This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for...