Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum and Braided Linear Algebra   Quantum matrices $A(R)$ are known for every $R$ matrix obeying the Quantum
Yang-Baxter Equations. It is also known that these act on `vectors' given by
the corresponding Zamalodchikov algebra. We develop this interpretation in
detail, distinguishing between two forms of this algebra, $V(R)$ (vectors) and
$V^*(R)$ (covectors). $A(R)\to V(R_{21})\tens V^*(R)$ is an algebra
homomorphism (i.e. quantum matrices are realized by the tensor product of a
quantum vector with a quantum covector), while the inner product of a quantum
covector with a quantum vector transforms as a scaler. We show that if $V(R)$
and $V^*(R)$ are endowed with the necessary braid statistics $\Psi$ then their
braided tensor-product $V(R)\und\tens V^*(R)$ is a realization of the braided
matrices $B(R)$ introduced previously, while their inner product leads to an
invariant quantum trace. Introducing braid statistics in this way leads to a
fully covariant quantum (braided) linear algebra. The braided groups obtained
from $B(R)$ act on themselves by conjugation in a way impossible for the
quantum groups obtained from $A(R)$.

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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
10
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: cmp-lg
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The categories of this paper are: adap-org