Characterizing nilpotent Lie algebras that satisfy the converse to the Schur theorem
Let L be a finite-dimensional nilpotent Lie algebra and d ( L / Z ( L )) be the minimal number generators for L / Z ( L ). It is known dim L / Z ( L ) = d ( L / Z ( L ) ) dim L 2 - t ( L ) for an integer t ( L ) ≥ 0 . In this paper, we classify all finite-dimensional nilpotent Lie algebras L when t...
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| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023-07, Vol.117 (3), Article 116 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
L
be a finite-dimensional nilpotent Lie algebra and
d
(
L
/
Z
(
L
)) be the minimal number generators for
L
/
Z
(
L
). It is known
dim
L
/
Z
(
L
)
=
d
(
L
/
Z
(
L
)
)
dim
L
2
-
t
(
L
)
for an integer
t
(
L
)
≥
0
.
In this paper, we classify all finite-dimensional nilpotent Lie algebras
L
when
t
(
L
)
∈
{
0
,
1
,
2
}
.
Moreover, we find a construction, which shows that there are Lie algebras of arbitrary
t
(
L
). |
|---|---|
| ISSN: | 1578-7303 1579-1505 |
| DOI: | 10.1007/s13398-023-01448-0 |