Coderivations, abelian extensions and cohomology of Lie coalgebras

2021 ◽  
pp. 1-24
Author(s):  
Lei Du ◽  
Youjun Tan
Keyword(s):  
Abelian Extensions

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.

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

Abelian extensions of partially ordered partial monoids

2012 ◽  
Vol 16 (8) ◽  
pp. 1339-1346 ◽  
Author(s):  
Sylvia Pulmannová ◽  
Elena Vinceková
Keyword(s):  
Abelian Extensions ◽  
Partially Ordered
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