Abelian extensions of leibniz algebras

1999 ◽  
Vol 27 (6) ◽  
pp. 2833-2846 ◽  
Author(s):  
J.M. Casas ◽  
E. Faro ◽  
A.M. Vieites
Keyword(s):  
Abelian Extensions ◽  
Leibniz Algebras

scholarly journals On non-abelian extensions of Leibniz algebras

2017 ◽  
Vol 46 (2) ◽  
pp. 574-587 ◽  
Author(s):  
Jiefeng Liu ◽  
Yunhe Sheng ◽  
Qi Wang
Keyword(s):  
Abelian Extensions ◽  
Leibniz Algebras

On solvable Leibniz algebras whose nilradical has characteristic sequence (m1,m2,m3)

2018 ◽  
Vol 2018 (3) ◽  
pp. 4-17
Author(s):  
K.K. Abdurasulov ◽  
Drew Horton ◽  
U.X. Mamadaliyev
Keyword(s):  
Characteristic Sequence ◽  
Leibniz Algebras

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

scholarly journals Naturally Graded 2-Filiform Leibniz Algebras

2010 ◽  
Vol 38 (10) ◽  
pp. 3671-3685 ◽  
Author(s):  
L. M. Camacho ◽  
J. R. Gómez ◽  
A. J. González ◽  
B. A. Omirov
Keyword(s):  
Leibniz Algebras

On Description of Leibniz Algebras Corresponding to sl 2

2012 ◽  
Vol 16 (5) ◽  
pp. 1507-1519 ◽  
Author(s):  
B. A. Omirov ◽  
I. S. Rakhimov ◽  
R. M. Turdibaev
Keyword(s):  
Leibniz Algebras
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