Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal measuring coalgebras and R - transformation algebras   Universal measuring coalgebras provide an enrichment of the category of
algebras over the category of coalgebras. By considering the special case of
the tensor algebra on a vector space V, the category of linear spaces itself
becomes enriched over coalgebras, and the universal measuring coalgebra is the
dual coalgebra of the tensor algebra T(V tensor V*). Given a braiding R on V
the universal measuring coalgebra P_R(V) which preserves the grading is
naturally dual to the Fadeev-Takhtadjhan-Reshitikin bialgebra A(R) and
therefore provides a representation of the quantized universal enveloping
algebra as an algebra of transformations. The action of P_R(V) descends to
actions on quotients of the tensor algebra, whenever the kernel of the quotient
map is preserved by the action of a generating subcoalgebra of P_R(V). This
allows representations of quantized enveloping algebras as transformation
groups of suitably quantized spaces.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: funct-an