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Bojko Bakalov, NC State, An operadic approach to vertex algebras and Poisson vertex algebras

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September 24, 2018 | 3:00 pm - 4:00 pm EDT

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Following Beilinson and Drinfeld, we describe vertex algebras as Lie algebras in a certain pseudo-tensor category. More
precisely, starting from a vector superspace V with a linear operator on it, we introduce the operad of n-ary chiral operations on V. When V is equipped with a vertex algebra structure, this allows us to define the cohomology of V with coefficients in a V-module. We introduce a filtration on the chiral operad and describe its associated graded operad in terms of acyclic graphs. We show that a Lie algebra for the latter operad is the same as a Poisson vertex algebra. This is a joint work with Alberto De Sole, Reimundo Heluani, and Victor Kac.

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Date

September 24, 2018

Time
3:00 pm - 4:00 pm
Event Category:
Location
SAS 4201