Derived bracket construction up to homotopy and Schroder numbers

2012/02/01 by Kyousuke Uchino, Uchino, K.
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.1202.0095

openalex publication_date 2012/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 construction of Leibniz operad. The theorem is proved by computing Schroder number.

Citations

• Universal enveloping algebras of Leibniz algebras and (co)homology
• Koszul duality for operads

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