Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential Batalin-Vilkovisky algebras arising from twilled
  Lie-Rinehart algebras   Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context,
complex structures on smooth manifolds. An almost complex manifold determines
an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the
almost complex structure is integrable. We characterize twilled LR structures
in terms of certain associated differential (bi)graded Lie and
G(erstenhaber)-algebras; in particular the G-algebra arising from an almost
complex structure is a d(ifferential) G-algebra iff the almost complex
structure is integrable. Such G-algebras, endowed with a generator turning them
into a B(atalin-)V(ilkovisky)-algebra, occur on the B-side of the mirror
conjecture. We generalize a result of Koszul to those dG-algebras which arise
from twilled LR-algebras. A special case thereof explains the relationship
between holomorphic volume forms and exact generators for the corresponding
dG-algebra and thus yields in particular a conceptual proof of the Tian-Todorov
lemma. We give a differential homological algebra interpretation for twilled
LR-algebras and by means of it we elucidate the notion of generator in terms of
homological duality for differential graded LR-algebras.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con