On graded and shifted notions, and thick morphisms

2025/06/20 by Voronov, Theodore
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2506.16920

Abstract

We consider the notions of L_∞-, P_∞-, and S_∞-algebras (including "shifted" versions) in the ℤ₂ × ℤ-graded setting. We also consider thick (microformal) morphisms and show how they work in such graded context. In particular, we show that a "shifted S_∞-thick morphism" (which we introduce here) induces an L_∞-morphism of shifted S_∞-structures. The same holds for "shifted P_∞-thick morphisms" and shifted P_∞-structures, respectively.

Citations

• A Graphical Calculus for Classical and Quantum Microformal Morphisms
• On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms
• An outline of shifted Poisson structures and deformation quantisation in derived differential geometry

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