Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotent Sabinin algebras   In this note we establish several basic properties of nilpotent Sabinin
algebras. Namely, we show that nilpotent Sabinin algebras (1) can be integrated
to produce nilpotent loops, (2) satisfy an analogue of the Ado theorem, (3)
have nilpotent Lie envelopes. We also give a new set of axioms for Sabinin
algebras. These axioms reflect the fact that a complementary subspace to a Lie
subalgebra in a Lie algebra is a Sabinin algebra. Finally, we note that the
non-associative version of the Jennings theorem produces a version of Ado
theorem for loops whose commutator-associator filtration is of finite length.

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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga