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Higher-order Bernstein algebras given by symmetric bilinear forms

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Higher-order Bernstein algebras given by symmetric bilinear forms. / Towers, David; Bowman, Kevin.
In: Linear Algebra and its Applications, Vol. 252, No. 1-3, 02.1997, p. 71-79.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Towers, D & Bowman, K 1997, 'Higher-order Bernstein algebras given by symmetric bilinear forms', Linear Algebra and its Applications, vol. 252, no. 1-3, pp. 71-79. https://doi.org/10.1016/0024-3795(95)00673-7

APA

Towers, D., & Bowman, K. (1997). Higher-order Bernstein algebras given by symmetric bilinear forms. Linear Algebra and its Applications, 252(1-3), 71-79. https://doi.org/10.1016/0024-3795(95)00673-7

Vancouver

Towers D, Bowman K. Higher-order Bernstein algebras given by symmetric bilinear forms. Linear Algebra and its Applications. 1997 Feb;252(1-3):71-79. doi: 10.1016/0024-3795(95)00673-7

Author

Towers, David ; Bowman, Kevin. / Higher-order Bernstein algebras given by symmetric bilinear forms. In: Linear Algebra and its Applications. 1997 ; Vol. 252, No. 1-3. pp. 71-79.

Bibtex

@article{cfbaff784777495d8f2d60cf01f4e497,
title = "Higher-order Bernstein algebras given by symmetric bilinear forms",
abstract = "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.",
author = "David Towers and Kevin Bowman",
year = "1997",
month = feb,
doi = "10.1016/0024-3795(95)00673-7",
language = "English",
volume = "252",
pages = "71--79",
journal = "Linear Algebra and its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",
number = "1-3",

}

RIS

TY - JOUR

T1 - Higher-order Bernstein algebras given by symmetric bilinear forms

AU - Towers, David

AU - Bowman, Kevin

PY - 1997/2

Y1 - 1997/2

N2 - 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.

AB - 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.

U2 - 10.1016/0024-3795(95)00673-7

DO - 10.1016/0024-3795(95)00673-7

M3 - Journal article

VL - 252

SP - 71

EP - 79

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - 1-3

ER -