Differential Graded Lie Algebras and Leibniz Algebra Cohomology
| Autor: | Jacob Mostovoy |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Leibniz algebra
Pure mathematics Functor Conjecture General Mathematics Mathematics::History and Overview Mathematics::Rings and Algebras 010102 general mathematics K-Theory and Homology (math.KT) Mathematics::Algebraic Topology 01 natural sciences Cohomology Mathematics::K-Theory and Homology Mathematics::Category Theory Mathematics - K-Theory and Homology 0103 physical sciences Lie algebra FOS: Mathematics 010307 mathematical physics 0101 mathematics Differential (mathematics) Mathematics |
| Zdroj: | International Mathematics Research Notices. 2022:196-209 |
| ISSN: | 1687-0247 1073-7928 |
| Popis: | 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]. |
| Databáze: | OpenAIRE |
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