Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493152 | Journal of Algebra | 2005 | 9 Pages |
Abstract
We prove that, if A is an absolute-valued â-algebra in the sense of [K. Urbanik, Absolute valued algebras with an involution, Fund. Math. 49 (1961) 247-258], then the normed space of A becomes a trigonometric algebra (in the meaning of [P.A. Terekhin, Trigonometric algebras, J. Math. Sci. (New York) 95 (1999) 2156-2160]) under the product ⧠defined by xâ§y:=(xâyâyâx)2. Moreover, we show that, “essentially,” all infinite-dimensional complete trigonometric algebras derive from absolute-valued â-algebras by the above construction method.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Julio Becerra Guerrero, Ángel RodrÃguez Palacios,