Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Geometry of Multi-Dirac Structures and Gerstenhaber Algebras   In a companion paper, we introduced a notion of multi-Dirac structures, a
graded version of Dirac structures, and we discussed their relevance for
classical field theories. In the current paper we focus on the geometry of
multi-Dirac structures. After recalling the basic definitions, we introduce a
graded multiplication and a multi-Courant bracket on the space of sections of a
multi-Dirac structure, so that the space of sections has the structure of a
Gerstenhaber algebra. We then show that the graph of a k-form on a manifold
gives rise to a multi-Dirac structure and also that this multi-Dirac structure
is integrable if and only if the corresponding form is closed. Finally, we show
that the multi-Courant bracket endows a subset of the ring of differential
forms with a graded Poisson bracket, and we relate this bracket to some of the
multisymplectic brackets found in the literature.

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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg