Let J be a special Jordan algebra and let cn(J) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain UJ2, the special Jordan algebra of 2×2 upper triangular matrices. As an immediate consequence, we prove that UJ2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
Martino, F. (2019). Varieties of special Jordan algebras of almost polynomial growth. JOURNAL OF ALGEBRA, 531, 184-196 [10.1016/j.jalgebra.2019.04.022].
Varieties of special Jordan algebras of almost polynomial growth
Martino, Fabrizio
2019-01-01
Abstract
Let J be a special Jordan algebra and let cn(J) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain UJ2, the special Jordan algebra of 2×2 upper triangular matrices. As an immediate consequence, we prove that UJ2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
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