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(n)(L) (V), n >= 1, be its Lcodimension sequence. If V is generated by a finite-dimensional L-algebra, then such a sequence is polynomially bounded only if V does not contain UT2, the 2 x 2 upper triangular matrix algebra with trivial L-action, and UT2 epsilon where L acts on UT2 as the 1-dimensional Lie algebra spanned by the inner derivation epsilon induced by e11. In this paper we completely classify all the L-subvarieties of var(L)(UT2) and var(L)(UT2 epsilon) by giving a complete list of finite-dimensional L-algebras generating them.

Martino, F., Rizzo, C. (2022). Differential Identities and Varieties of Almost Polynomial Growth. ISRAEL JOURNAL OF MATHEMATICS [10.1007/s11856-022-2396-1].

Differential Identities and Varieties of Almost Polynomial Growth

Martino, F
Primo
;
2022-01-01

Abstract

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(n)(L) (V), n >= 1, be its Lcodimension sequence. If V is generated by a finite-dimensional L-algebra, then such a sequence is polynomially bounded only if V does not contain UT2, the 2 x 2 upper triangular matrix algebra with trivial L-action, and UT2 epsilon where L acts on UT2 as the 1-dimensional Lie algebra spanned by the inner derivation epsilon induced by e11. In this paper we completely classify all the L-subvarieties of var(L)(UT2) and var(L)(UT2 epsilon) by giving a complete list of finite-dimensional L-algebras generating them.
2022
Martino, F., Rizzo, C. (2022). Differential Identities and Varieties of Almost Polynomial Growth. ISRAEL JOURNAL OF MATHEMATICS [10.1007/s11856-022-2396-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/585092
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