Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple Commutator Formulas   Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite
algebras) with identity. Let I_i, i=0,...,m, be two-sided ideals of A,
\GL_n(A,I_i) the principal congruence subgroup of level I_i in GL_n(A) and
E_n(A,I_i) be the relative elementary subgroup of level I_i. We prove a
multiple commutator formula
  [E_n(A,I_0),\GL_n(A,I_1),& \GL_n(A, I_2),..., \GL_n(A, I_m)] =
[E_n(A,I_0),E_n(A,I_1),E_n(A, I_2),..., E_n(A, I_m)],
  which is a broad generalization of the standard commutator formulas.

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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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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: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an