Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras

Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebras and Representation Theory Springer Journals

Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Mathematics; Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras
ISSN
1386-923X
eISSN
1572-9079
D.O.I.
10.1007/s10468-017-9731-y
Publisher site
See Article on Publisher Site

Abstract

We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work.

Journal

Algebras and Representation TheorySpringer Journals

Published: Sep 5, 2017

References

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