On commutative isotopes of Jordan algebra of a symmetric bilinear nondegenerate form on a two-dimensional vector space

Vita Glizburg; Sergey Pchelintsev

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arXiv · 2504.00868

On commutative isotopes of Jordan algebra of a symmetric bilinear nondegenerate form on a two-dimensional vector space

Vita Glizburg·Sergey Pchelintsev

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Abstract

In the article we study the simple unital communitative three-dimensional algebras over an algebraically closed field of characteristic not equal to 2. It is proved that every simple unital communitative three-dimensional algebra of nil-rank 2 is isotopic to Jordan algebra of a symmetric bilinear nondegenerate form on a two-dimensional vector space.

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Vita Glizburg, Sergey Pchelintsev. 2025-04-01. On commutative isotopes of Jordan algebra of a symmetric bilinear nondegenerate form on a two-dimensional vector space. https://arxiv.org/abs/2504.00868

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