Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Loop Groups to 2-Groups   We describe an interesting relation between Lie 2-algebras, the Kac-Moody
central extensions of loop groups, and the group String(n). A Lie 2-algebra is
a categorified version of a Lie algebra where the Jacobi identity holds up to a
natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a
categorified version of a Lie group. If G is a simply-connected compact simple
Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having
Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the
canonical 3-form on G. There appears to be no Lie 2-group having g_k as its Lie
2-algebra, except when k = 0. Here, however, we construct for integral k an
infinite-dimensional Lie 2-group whose Lie 2-algebra is equivalent to g_k. The
objects of this 2-group are based paths in G, while the automorphisms of any
object form the level-k Kac-Moody central extension of the loop group of G.
This 2-group is closely related to the kth power of the canonical gerbe over G.
Its nerve gives a topological group that is an extension of G by K(Z,2). When k
= +-1, this topological group can also be obtained by killing the third
homotopy group of G. Thus, when G = Spin(n), it is none other than String(n).

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph