Higher-order Bernstein algebras given by symmetric bilinear forms

Towers, David and Bowman, Kevin (1997) Higher-order Bernstein algebras given by symmetric bilinear forms. Linear Algebra and its Applications, 252 (1-3). pp. 71-79. ISSN 0024-3795

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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.

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Journal Article
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Linear Algebra and its Applications
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28 Sep 2011 15:43
Last Modified:
21 Nov 2022 21:41