Finite-Dimensional Ternary Algebras
Abstract
A ternary algebra is a linear space Alpha over the complex numbers such that for any three elements A, B and C in Alpha there exists a product AB*C in Alpha satisfying certain axioms which reduce to ordinary properties of matrix multiplication when the elements of Alpha are matrices and * denotes conjugate transpose. The present paper is devoted to a study of the algebraic structure of ternary algebras. In particular it is shown that an arbitrary finite-dimensional ternary algebra has a representation as a ternary algebra of matrices.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1967
- Accession Number
- AD0674312
Entities
People
- Howard B. Ritea
Organizations
- University of California, Los Angeles