2019/04/13 by Matthew Burke, Burke, Matthew, Benjamin MacAdam +1
Mathematics · #18F99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1904.06594
openalex publication_date 2019/04/13 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We define involution algebroids which generalise Lie algebroids to the\nabstract setting of tangent categories. As a part of this generalisation the\nJacobi identity which appears in classical Lie theory is replaced by an\nidentity similar to the Yang-Baxter equation. Every classical Lie algebroid has\nthe structure of an involution algebroid and every involution algebroid in a\ntangent category admits a Lie bracket on the sections of its underlying bundle.\nAs an illustrative application we take the first steps in developing the\nhomotopy theory of involution algebroids.\n