# Homotopy Poisson-n Algebras from N-plectic Structures

@article{Richter2015HomotopyPA, title={Homotopy Poisson-n Algebras from N-plectic Structures}, author={Mirco Richter}, journal={arXiv: Differential Geometry}, year={2015} }

We associate a homotopy Poisson-n algebra to any higher symplectic structure, which generalizes the common symplectic Poisson algebra of smooth functions. This provides robust n-plectic prequantum data for most approaches to quantization.

## One Citation

### Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time

- MathematicsSymmetry
- 2019

The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical…

## References

SHOWING 1-10 OF 17 REFERENCES

### On the universal enveloping algebra of a Lie algebroid

- Mathematics
- 2010

We review the extent to which the structure of the universal enveloping algebra of a Lie algebroid over a manifold M resembles a Hopf algebra, and prove a Cartier-Milnor-Moore theorem for this type…

### Homotopy algebra and iterated integrals for double loop spaces

- Mathematics
- 1994

This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended…

### THE POISSON BRACKET FOR POISSON FORMS IN MULTISYMPLECTIC FIELD THEORY

- Mathematics
- 2003

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and,…

### Higher Symplectic Geometry

- Mathematics
- 2011

Author(s): Rogers, Christopher Lee | Advisor(s): Baez, John C | Abstract: In higher symplectic geometry, we consider generalizations of symplectic manifolds called n-plectic manifolds. We say a…

### Poisson cohomology and quantization.

- Mathematics
- 1990

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending…

### Homotopy Batalin–Vilkovisky algebras

- Mathematics
- 2009

This paper provides an explicit cobrant resolution of the operad encoding Batalin{Vilkovisky algebras. Thus it denes the notion of homotopy Batalin{Vilkovisky algebras with the required homotopy…

### DIFFERENTIAL FORMS ON GENERAL COMMUTATIVE ALGEBRAS

- Mathematics
- 1963

Introduction. Let K be a commutative ring with ulnit, and let R be a commutative unitary K-algebra. We shall be concerned with variously defined cohomology theories based on algebras of differential…

### Loop Spaces, Characteristic Classes and Geometric Quantization

- Mathematics
- 1994

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical…