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- Title
Jordan–Kronecker Invariants for Lie Algebras of Small Dimensions.
- Authors
Groznova, A. Yu.
- 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).
- Subjects
LIE algebras; MATRIX pencils; VECTOR spaces; POISSON brackets; COMMERCIAL space ventures; SYMMETRIC matrices
- Publication
Journal of Mathematical Sciences, 2023, Vol 269, Issue 4, p492
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-023-06295-3