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Jordan–Kronecker Invariants for Lie Algebras of Small Dimensions.
- Source :
-
Journal of Mathematical Sciences . Jan2023, Vol. 269 Issue 4, p492-502. 11p. - Publication Year :
- 2023
-
Abstract
- In this paper, Jordan–Kronecker invariants are calculated for all nilpotent 6- and 7-dimensional Lie algebras. We consider the Poisson bracket family, depending on the lambda parameter on a Lie coalgebra, i.e., on the linear space dual to a Lie algebra. For some space 픤 proposed in the paper, two skew-symmetric matrices are defined for all points x on this linear space. To understand the behaviour of the matrix pencil (A − λB)(x), we consider Jordan–Kronecker invariants for this pencil and how they change with x (the latter is done for 6-dimensional Lie algebras). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 269
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 162181852
- Full Text :
- https://doi.org/10.1007/s10958-023-06295-3