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Joint spectra and nilpotent Lie algebras of linear transformations
- Source :
- Enrico Boasso, Scopus-Elsevier
-
Abstract
- Given a complex nilpotent finite dimensional Lie algebra of linear transformations $L$, in a complex finite dimensional vector space $E$, we study the joint spectra $Sp(L,E)$, $\sigma_{\delta,k}(L,E)$ and $\sigma_{\pi,k}(L,E)$. We compute them and we prove that they all coincide with the set of weights of $L$ for $E$. We also give a new interpretation of some basic module operations of the Lie algebra $L$ in terms of the joint spectra.<br />Comment: 10 pages, original research article
- Subjects :
- Discrete mathematics
Pure mathematics
Numerical Analysis
Algebra and Number Theory
Simple Lie group
Adjoint representation
Universal enveloping algebra
Affine Lie algebra
Graded Lie algebra
Lie conformal algebra
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Lie coalgebra
Adjoint representation of a Lie algebra
Primary 47A13, Secondary 15A04, 17B30
FOS: Mathematics
Discrete Mathematics and Combinatorics
Geometry and Topology
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Enrico Boasso, Scopus-Elsevier
- Accession number :
- edsair.doi.dedup.....c8f863bc80876e981d59bf1afd73ca6e