Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-Dimensional Algebra VI: Lie 2-Algebras   The theory of Lie algebras can be categorified starting from a new notion of
"2-vector space", which we define as an internal category in Vect. There is a
2-category 2Vect having these 2-vector spaces as objects, "linear functors" as
morphisms and "linear natural transformations" as 2-morphisms. We define a
"semistrict Lie 2-algebra" to be a 2-vector space L equipped with a
skew-symmetric bilinear functor satisfying the Jacobi identity up to a
completely antisymmetric trilinear natural transformation called the
"Jacobiator", which in turn must satisfy a certain law of its own. This law is
closely related to the Zamolodchikov tetrahedron equation, and indeed we prove
that any semistrict Lie 2-algebra gives a solution of this equation, just as
any Lie algebra gives a solution of the Yang-Baxter equation. We construct a
2-category of semistrict Lie 2-algebras and prove that it is 2-equivalent to
the 2-category of 2-term L-infinity algebras in the sense of Stasheff. We also
study strict and skeletal Lie 2-algebras, obtaining the former from strict Lie
2-groups and using the latter to classify Lie 2-algebras in terms of 3rd
cohomology classes in Lie algebra cohomology. This classification allows us to
construct for any finite-dimensional Lie algebra g a canonical 1-parameter
family of Lie 2-algebras g_hbar which reduces to g at hbar = 0. These are
closely related to the 2-groups G_hbar constructed in a companion paper.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: eess