Varieties of special Jordan algebras of almost polynomial growth

Martino, Fabrizio

doi:10.1016/j.jalgebra.2019.04.022

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2022

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“…Varieties of poylnomial growth were extensively studied in the past years in various settings. We refer the interested reader to [5], [6], [22] for some results about ordinary algebras; to [8], [23], [24], [32] for superalgebras and more generally group graded algebras; to [3], [7], [10], [20], [21], [25] for algebras with involution, graded involution, superinvolution and pseudoinvolution; to [27] for special Jordan algebras.…”

Section: Introductionmentioning

confidence: 99%

Differential identities and varieties of almost polynomial growth

Martino

Rizzo

2022

Isr. J. Math.

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Let V be an L-variety of associative L-algebras, i.e., algebras where a Lie algebra L acts on them by derivations, and let c L n (V), n ≥ 1, be its L-codimension sequence. If V is generated by a finite dimensional L-algebra, then such a sequence is polynomially bounded if and only if V does not contain U T 2 , the 2 × 2 upper triangular matrix algebra with trivial L-action, and U T ε 2 where L acts on U T 2 as the 1-dimensional Lie algebra spanned by the inner derivation ε induced by e 11 . In this paper we completely classify all the L-subvarieties of var L (U T 2 ) and var L (U T ε2 ) by giving a complete list of finite dimensional L-algebras generating them.

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