2024/01/11 by Branislav Jurčo, Jurčo, Branislav, Ján Pulmann +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2401.06110
openalex publication_date 2024/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum L_∞ algebras are higher loop generalizations of cyclic L_∞ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of (-1)-shifted symplectic vector spaces and distributional half-densities, originally proposed by Ševera. Morphisms in this category can be given both by formal half-densities and Lagrangian relations; we prove that the composition of such morphisms recovers the construction of homotopy transfer of quantum L_∞ algebras. Finally, using this category, we propose a new notion of a relation between quantum L_∞ algebras.