Invariants of real low dimension Lie algebras

DOI10.1063/1.522992zbMath0357.17004OpenAlexW2069185213WikidataQ115188656 ScholiaQ115188656MaRDI QIDQ4129601

R. T. Sharp, Hans J. Zassenhaus, Pavel Winternitz, Jirí Patera

Publication date: 1976

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.522992

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05) Applications of Lie groups to the sciences; explicit representations (22E70) Solvable, nilpotent (super)algebras (17B30)

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Cites Work