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Doctoral Thesis
Document
Author
Full name
Pryscilla dos Santos Ferreira Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Mencattini, Igor (President)
Gonzalez, Cristian Andres Ortiz
Levcovitz, Daniel
Quesney, Alexandre Thomas Guillaume
Title in English
A post-Lie operad of rooted trees
Keywords in English
Enveloping algebra
Operads
Post-Lie algebra
Rooted trees
Abstract in English
In this thesis we propose a description of the operad defining post-Lie algebras in terms of rooted trees and we discuss some applications of such a construction. In particular, we re-derive both the free post-Lie algebra defined in [22] and the main result of the paper [8]. Furthermore, a possible extension of the concept of symmetric brace algebra to the category of the post-Lie algebras is proposed.
Title in Portuguese
Uma operad pós-Lie de árvores enraizadas
Keywords in Portuguese
Álgebra envolvente
Álgebra pós-Lie
Árvores enraizadas
Operads
Abstract in Portuguese
Nessa tese propomos a descrição da operad que define as álgebras pós-Lie em termos de árvores enraizadas e discutimos algumas aplicações dessa construção. Em particular, nós obtemos novamente a álgebra pós-Lie livre definida em [22] e o resultado principal do artigo [8]. Além disso, uma possível extensão do conceito de álgebra brace simétrica à categoria de álgebras pós-Lie é apresentada.
 
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Publishing Date
2018-10-11
 
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