Encyclopedia of types of algebras 2010

@article{Zinbiel2010EncyclopediaOT,
title={Encyclopedia of types of algebras 2010},
author={Guillaume W. Zinbiel},
journal={arXiv: Rings and Algebras},
year={2010}
}
This is a cornucopia of types of algebras with some of their properties from the operadic point of view.
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
Dual Alternative Algebras in Characteristic Three
We prove that the dimension of the arity n component of the operad of dual alternative algebras over a field of characteristic three is equal to 2 n − n, and describe the structure of the
On some basic properties of Leibniz algebras
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results
A trick to compute certain Manin products of operads
We describe simple tricks to compute the Manin black products with the operads $\mathcal{A}ss$, $\mathcal{C}om$ and $pre\mathcal{L}ie$.
Five interpretations of Fa\`a di Bruno's formula
• Mathematics, Physics
• 2011
In these lectures we present five interpretations of the Fa' di Bruno formula which computes the n-th derivative of the composition of two functions of one variable: in terms of groups, Lie algebras
Universal enveloping commutative Rota-Baxter algebras of precommutative and postcommutative algebras
Universal enveloping commutative Rota—Baxter algebras of preand postcommutative algebras are constructed. The pair of varieties (RBλCom,postCom) is proved to be a PBW-pair and the pair (RBCom,preCom)
Derived bracket construction up to homotopy and Schroder numbers
We will introduce the notion of higher derived bracket construction in the category of operads and prove that the higher derived bracket construction of Lie operad is equivalent to the cobar