Infinite dimensional quadratic forms admitting composition
Alberto Elduque,Alberto Elduque,José María López Pérez +2 more
- 01 Jan 1997
- Vol. 125, Iss: 8, pp 2207-2216
TL;DR: In this paper, those composition algebras with a one-sided unit element are characterized and examples are given of arbitrary infinite dimension, where the unit element is a unit unit element.
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Abstract: Composition algebras with a unit element constitute a well-known class of algebras. In this paper, those composition algebras with a one-sided unit element are characterized and examples are given of arbitrary infinite dimension.
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Citations
Absolute-Valued Algebraic Algebras Are Finite-Dimensional
TL;DR: In this paper, it was shown that if A is a non-associative algebra over the field of real numbers, and if there is a norm on A satisfying xy = x, y for all x, y in A, then A is finite-dimensional.
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Composition Algebras with Large Derivation Algebras
TL;DR: In this article, the authors studied the composition algebras with large derivation algebraes and classified them into different classes: the para-Hurwitz, the Okubo, and the Hurwitz.
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•Posted Content
Some examples of division symbol algebras of degree 3 and 5
Cristina Flaut,Diana Savin +1 more
TL;DR: In this paper, the product between two elements in a symbol algebra of degree n and an octonion non-division algebra was computed in the symbol algebra with degree 3 and degree 5, respectively.
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Composition algebras of degree two
Alberto Elduque,José M. Pérez-izquierdo +1 more
- 01 Oct 1999
TL;DR: Composition algebras in which the subalgebra generated by any element has dimension at most two are classified over fields of characteristic as discussed by the authors, which include, besides the classical unital composition algebra, some closely related composition algebraic classes, and all the composition algebraic classes with invariant quadratic norm.
13
Power associative composition algebras
TL;DR: In this article, the authors extend Okubo's result to composition algebras satisfying (x, x, x) = 0 over a field of characteristic not 2 which contains at least four elements.
11
References
One-sided division absolute valued algebras
TL;DR: In this article, a structure theory for left divsion absolute valued algebras is developed, which shows that the norm of such an algebra comes from an inner product.