Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quotient of a Kauffman bracket skein algebra by the square of an
  augmentation ideal   We give an explicit basis $\mathcal{B}$ of the quotient of the Kauffman
bracket skein algebra $\mathcal{S} (\Sigma)$ on a surface $\Sigma$ by the
square of an augmentation ideal. As an application, it induces two kinds of
finite type invariants of links in a handle body in the sense of Le. Moreover,
we construct an embedding of the mapping class group of a compact connected
surface of genus $0$ into the Kauffman bracket skein algebra on the surface
completed with respect to a filtration coming from the augmentation ideal.

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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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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: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex