Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Frobenius homomorphism for Lusztig's quantum groups over arbitrary
  roots of unity   For a finite dimensional semisimple Lie algebra and a root of unity, Lusztig
defined an infinite dimensional quantum group of divided powers. Under certain
restrictions on the order of the root of unity, he constructed a Frobenius
homomorphism with finite dimensional Hopf kernel and with image the universal
enveloping algebra.
  In this article we define and describe the Frobenius homomorphism for
arbitrary roots of unity by systematically using the theory of Nichols
algebras. In several new exceptional cases the Frobenius-Lusztig kernel is
associated to a different Lie algebra than the initial Lie algebra. Moreover,
the Frobenius homomorphism often switches short and long roots, and may produce
Lie algebras in a symmetrically braided category.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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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: solv-int
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The categories of this paper are: gr-qc