leibniz cohomology
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2021 ◽  
Vol 569 ◽  
pp. 276-317
Author(s):  
Jörg Feldvoss ◽  
Friedrich Wagemann
Keyword(s):  

2020 ◽  
Vol 28 (2) ◽  
pp. 123-137
Author(s):  
Friedrich Wagemann

AbstractWe construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2. In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley--Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.


Author(s):  
Jacob Mostovoy

Abstract In this note, we interpret Leibniz algebras as differential graded (DG) Lie algebras. Namely, we consider two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley–Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in [ 9].


2019 ◽  
Vol 26 (02) ◽  
pp. 271-284 ◽  
Author(s):  
Goutam Mukherjee ◽  
Ripan Saha

We study finite group actions on Leibniz algebras, and define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology, which makes it a graded Zinbiel algebra.


2018 ◽  
Vol 17 (12) ◽  
pp. 1850222 ◽  
Author(s):  
J. Q. Adashev ◽  
M. Ladra ◽  
B. A. Omirov

In this paper, we prove some general results on Leibniz 2-cocyles for simple Leibniz algebras. Applying these results, we prove the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to [Formula: see text].


2014 ◽  
Vol 13 (08) ◽  
pp. 1450052 ◽  
Author(s):  
Yan Wang ◽  
Yufeng Pei ◽  
Shaoqiang Deng

In this paper, we develop a general theory on Leibniz central extensions of Lie superalgebras and apply it to determine the second Leibniz cohomology groups for several classes of Lie superalgebras, including classical Lie superalgebras, Neveu–Schwarz superalgebras, differentiably simple Lie superalgebras, and affine (toroidal) Kac–Moody Lie superalgebras.


2013 ◽  
Vol 195 (4) ◽  
pp. 481-485 ◽  
Author(s):  
E. Khmaladze
Keyword(s):  

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