Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Courant-Dorfman algebras and their cohomology   We introduce a new type of algebra, the Courant-Dorfman algebra. These are to
Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson
algebras to Poisson manifolds. We work with arbitrary rings and modules,
without any regularity, finiteness or non-degeneracy assumptions. To each
Courant-Dorfman algebra $(\R,\E)$ we associate a differential graded algebra
$\C(\E,\R)$ in a functorial way by means of explicit formulas. We describe two
canonical filtrations on $\C(\E,\R)$, and derive an analogue of the Cartan
relations for derivations of $\C(\E,\R)$; we classify central extensions of
$\E$ in terms of $H^2(\E,\R)$ and study the canonical cocycle
$\Theta\in\C^3(\E,\R)$ whose class $[\Theta]$ obstructs re-scalings of the
Courant-Dorfman structure. In the nondegenerate case, we also explicitly
describe the Poisson bracket on $\C(\E,\R)$; for Courant-Dorfman algebras
associated to Courant algebroids over finite-dimensional smooth manifolds, we
prove that the Poisson dg algebra $\C(\E,\R)$ is isomorphic to the one
constructed in \cite{Roy4-GrSymp} using graded manifolds.

34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas