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On the capability and Schur multiplier of nilpotent Lie algebra of class two


Authors: Peyman Niroomand, Farangis Johari and Mohsen Parvizi
Journal: Proc. Amer. Math. Soc. 144 (2016), 4157-4168
MSC (2010): Primary 17B30; Secondary 17B05, 17B99
DOI: https://doi.org/10.1090/proc/13092
Published electronically: May 6, 2016
MathSciNet review: 3531169
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Abstract: Recently, the authors in a joint paper obtained the structure of all capable nilpotent Lie algebras with derived subalgebra of dimension at most $ 1$. This paper is devoted to characterizing all capable nilpotent Lie algebras of class two with derived subalgebra of dimension $ 2$. It develops and generalizes the result due to Heineken for the group case.


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Additional Information

Peyman Niroomand
Affiliation: School of Mathematics and Computer Science, Damghan University, Damghan, Iran
Email: niroomand@du.ac.ir, p$_$niroomand@yahoo.com

Farangis Johari
Affiliation: Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Email: farangis.johari@stu.um.ac.ir

Mohsen Parvizi
Affiliation: Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Email: parvizi@math.um.ac.ir

DOI: https://doi.org/10.1090/proc/13092
Keywords: Nilpotent Lie algebra, Schur multiplier, capable Lie algebra
Received by editor(s): August 31, 2015
Received by editor(s) in revised form: December 21, 2015
Published electronically: May 6, 2016
Additional Notes: The first author acknowledges the financial support of the research council of Damghan University with the grant number 93/math/127/229.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2016 American Mathematical Society