Shifted symplectic Lie algebroids

Brent Pym, Pavel Safronov

Research output: Contribution to journalArticlepeer-review


Shifted symplectic Lie and L∞ algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical AKSZ topological field theory. In this paper, we classify zero-, one- and two-shifted symplectic algebroids and their higher gauge symmetries, in terms of classical geometric "higher structures", such as Courant algebroids twisted by Ω2-gerbes. As applications, we produce new examples of twisted Courant algebroids from codimension-two cycles, and we give symplectic interpretations for several well known features of higher structures (such as twists, Pontryagin classes, and tensor products). The proofs are valid in the C∞, holomorphic and algebraic settings, and are based on a number of technical results on the homotopy theory of L∞ algebroids and their differential forms, which may be of independent interest.
Original languageEnglish
Pages (from-to) 7489–7557
Number of pages60
JournalInternational Mathematics Research Notices
Issue number21
Publication statusPublished - 7 Sep 2018


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