Higher Lie and Leibniz algebras
David Khudaverdyan
TL;DR
This paper explores advanced algebraic structures like higher Lie and Leibniz algebras, focusing on their abstractions, categorifications, and applications in mathematics and physics.
Contribution
It provides new insights into the homotopification and categorification of algebraic operads and higher structures, advancing the theoretical framework.
Findings
Developed new models for higher Lie and Leibniz algebras
Enhanced understanding of homotopy and categorification in algebraic structures
Bridged concepts between mathematics and physics in higher gauge theories
Abstract
Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in Mathematics and Physics. The present thesis deals with abstractions and flexibilizations of algebraic structures, and more precisely, with algebraic operads, homotopification and categorification.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models