Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electrical networks and Lie theory   We introduce a new class of "electrical" Lie groups. These Lie groups, or
more precisely their nonnegative parts, act on the space of planar electrical
networks via combinatorial operations previously studied by
Curtis-Ingerman-Morrow. The corresponding electrical Lie algebras are obtained
by deforming the Serre relations of a semisimple Lie algebra in a way suggested
by the star-triangle transformation of electrical networks. Rather
surprisingly, we show that the type A electrical Lie group is isomorphic to the
symplectic group. The nonnegative part (EL_{2n})_{\geq 0} of the electrical Lie
group is a rather precise analogue of the totally nonnegative subsemigroup
(U_{n})_{\geq 0} of the unipotent subgroup of SL_{n}. We establish
decomposition and parametrization results for (EL_{2n})_{\geq 0}, paralleling
Lusztig's work in total nonnegativity, and work of Curtis-Ingerman-Morrow and
de Verdi\`{e}re-Gitler-Vertigan for networks. Finally, we suggest a
generalization of electrical Lie algebras to all Dynkin types.

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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc