Automorphisms of Strong Homotopy Lie Algebras of Local Observables

Abstract

There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting Lie 2-algebra is isomorphic to a sub Lie 2-algebra of a natural Lie 2-algebra structure on an exact Courant algebroid. We generalize this statement to arbitrary n-plectic manifolds and study automorphisms on the arising Lie n-algebras. Our observations may be useful in studying the quantization problem on multisymplectic manifolds.

arXiv comment1+28 pages

References in corpus (8)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• Some title containing the words "homotopy" and "symplectic", e.g. this one
• Courant Algebroids and Strongly Homotopy Lie Algebras
• Higher Symplectic Geometry
• Generalizing Geometry - Algebroids and Sigma Models
• Groupoid Quantization of Loop Spaces
• Lie 2-algebra models

Cited by in corpus (3)

• AKSZ constructions for topological membranes on $G_2$-manifolds
• Generalized Higher Gauge Theory
• Brane current algebras and generalised geometry from QP manifolds