Titulo: Higher Koszul brackets on the cotangent complex

Data: 28/07/2022
Horário: 15h
Local: Sala C119

Resumo: Let A=k[x1,x2,…,xn]/I be a commutative algebra where k is a field, char(k)=0⁠, and I⊆S:=k[x1,x2,…,xn] a Poisson ideal. It is well known that [dxi,dxj]:=d{xi,xj} defines a Lie bracket on the A-module ΩA|k of Kähler differentials, making (A,ΩA|k) a Lie–Rinehart pair. If A is not regular, that is, ΩA|k is not projective, the cotangent complex LA|k serves as a replacement for ΩA|k⁠. We prove that LA|k is an L∞-algebroid compatible with the Lie–Rinehart pair (A,ΩA|k)⁠. The L∞-algebroid structure comes from a P∞-algebra structure on the resolvent of the morphism S→A. We identify examples when this L∞-algebroid simplifies to a dg Lie algebroid, concentrating on cases where S is Z≥0-graded and I and {,} are homogeneous.

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Meeting ID: 884 0114 9276
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