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1
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1answer
87 views

universal enveloping algebra of Leibniz algebra

According to Loday and Prashvili's paper, to defined universal enveloping algebra of Leibniz algebras we need $g^{r}$ and $g^{l}$ as two copies of the Leibniz algebra $g$. What does it mean by ...
3
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0answers
45 views

filteration for Leibniz algebras [closed]

Let $L$ be restricted Lie algebra, we define p-filteration $$ L=L_{1} \supseteq L_{1} ... \supseteq L_{n}... $$, satisfying the following conditions: $ [L_{i},L_{j}] \subseteq L_{i+j}$ and $L_{i}^{[p]...
6
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1answer
153 views

Which known theorems of Lie algebras are still valid for Leibniz algebras?

Leibniz algebras can be seen as a non-commutative generalization of Lie algebras. Thus, it is common to see a lot of papers which topic is about a generalization of a classic theorem of Lie algebras ...
2
votes
1answer
847 views

Automorphism theorem

Help me please to find reference for the proof of the following theorem: Theorem. Let $\theta$ be a Leibniz cocycle on the Leibniz algebra L with values in $V,$ and assume $\theta^{\bot}\cap C(L)=(0)....
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3answers
279 views

classification of Nilpotent Leibniz Algebra

I am interested about the last results belong to the classification of the low dimensional Leibniz algebra. Does anybody can help me?
8
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3answers
952 views

Hopf algebra structure on the universal enveloping algebra of a Leibniz algebra?

A Leibniz algebra L may be thought of as a noncommutative generalisation of a Lie algebra. One drops the requirement that the bracket be alternating and substitutes the Jacobi identity for the ...