Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Divided Power Algebra, q-Derivatives and Some New Quantum Groups   The discussions in the present paper arise from exploring intrinsically the
structure nature of the quantum $n$-space. A kind of braided category $\Cal
{GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$
is established. The quantum divided power algebra over $k$ related to the
quantum $n$-space is introduced and described as a braided Hopf algebra in
$\Cal {GB}$ (in terms of its 2-cocycle structure), over which the so called
special $q$-derivatives are defined so that several new interesting quantum
groups, especially, the quantized polynomial algebra in $n$ variables (as the
quantized universal enveloping algebra of the abelian Lie algebra of dimension
$n$), and the quantum group associated to the quantum $n$-space, are derived
from our approach independently of using the $R$-matrix. As a verification of
its validity of our discussion, the quantum divided power algebra is equipped
with a structure of $U_q(\frak {sl}_n)$-module algebra via a certain
$q$-differential operators realization. Particularly, one of the four kinds of
roots vectors of $U_q(\frak {sl}_n)$ in the sense of Lusztig can be specified
precisely under the realization.

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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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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: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn