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arXiv · 1209.6544

Two-generated algebras and standard-form congruence

Jason Gaddis
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Abstract

Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic polynomials. Canonical forms under standard-form congruence for three-by-three matrices are derived. This is then used to give a classification of algebras defined by two generators and one degree two relation. We also apply standard-form congruence to classify homogenizations of these algebras.

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Jason Gaddis. 2012-09-28. Two-generated algebras and standard-form congruence. https://doi.org/10.1080/00927872.2013.876034

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