Solvable extensions of a special class of nilpotent Lie algebras

A. Shabanskaya; Gerard Thompson

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 3, page 141-159
  • ISSN: 0044-8753

Abstract

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A pair of sequences of nilpotent Lie algebras denoted by and are introduced. Here denotes the dimension of the algebras that are defined for ; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of and all possible solvable extensions are constructed so that and serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating solvable Lie algebras using special properties rather than trying to extend one dimension at a time.

How to cite

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Shabanskaya, A., and Thompson, Gerard. "Solvable extensions of a special class of nilpotent Lie algebras." Archivum Mathematicum 049.3 (2013): 141-159. <http://eudml.org/doc/260663>.

@article{Shabanskaya2013,
abstract = {A pair of sequences of nilpotent Lie algebras denoted by $N_\{n,11\}$ and $N_\{n,19\}$ are introduced. Here $n$ denotes the dimension of the algebras that are defined for $n\ge 6$; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of $N_\{n,11\}$ and $N_\{n,19\}$ all possible solvable extensions are constructed so that $N_\{n,11\}$ and $N_\{n,19\}$ serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating solvable Lie algebras using special properties rather than trying to extend one dimension at a time.},
author = {Shabanskaya, A., Thompson, Gerard},
journal = {Archivum Mathematicum},
keywords = {solvable Lie algebra; nilradical; derivation; solvable Lie algebra; nilradical; derivation},
language = {eng},
number = {3},
pages = {141-159},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Solvable extensions of a special class of nilpotent Lie algebras},
url = {http://eudml.org/doc/260663},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Shabanskaya, A.
AU - Thompson, Gerard
TI - Solvable extensions of a special class of nilpotent Lie algebras
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 3
SP - 141
EP - 159
AB - A pair of sequences of nilpotent Lie algebras denoted by $N_{n,11}$ and $N_{n,19}$ are introduced. Here $n$ denotes the dimension of the algebras that are defined for $n\ge 6$; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of $N_{n,11}$ and $N_{n,19}$ all possible solvable extensions are constructed so that $N_{n,11}$ and $N_{n,19}$ serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating solvable Lie algebras using special properties rather than trying to extend one dimension at a time.
LA - eng
KW - solvable Lie algebra; nilradical; derivation; solvable Lie algebra; nilradical; derivation
UR - http://eudml.org/doc/260663
ER -

References

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