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Higher-order Bernstein algebras given by symmetric bilinear forms

Research output: Contribution to journalJournal article

<mark>Journal publication date</mark>02/1997
<mark>Journal</mark>Linear Algebra and its Applications
Issue number1-3
Number of pages9
Pages (from-to)71-79
<mark>Original language</mark>English


Let (A, ω) be a kth-order Bernstein algebra and let N be the kernel of ω. This article studies the structure of such algebras in which N2 has dimension one. The algebras are of two types, I and II, according as N2 ⊆ U or N2 ⊈ U. A characterization of the algebras of type I is given. Power associative kth-order Bernstein algebras with dim N2 = 1 are then considered: they turn out to be Bernstein algebras of at most second order, and multiplication tables for these algebras over the real field are given. Finally, second-order Bernstein algebras of type II are examined and a structure theorem for them is obtained.