Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On certain lattices associated with generic division algebras   Let S_n denote the symmetric group on n letters. We consider the S_n-root
lattice A_{n-1} = {(z1,...,zn) in Z^n | z1+...+zn = 0}, where S_n acts on Z^n
by permuting the coordinates, and its tensor, symmetric, and exterior squares.
For odd values of n, we show that the tensor square is equivalent, in the sense
of Colliot-Thelene and Sansuc, to the exterior square. Consequently, the
rationality problem for generic division algebras, for odd values of n, amounts
to proving stable rationality of the multiplicative S_n-invariant field of the
exterior square of A_{n-1}. Furthermore, confirming a conjecture of Le Bruyn,
we show that n=2 and n=3 are the only cases where the tensor square of A_{n-1}
is equivalent to a permutation S_n-lattice. In the course of the proof of this
result, we construct subgroups H of S_n, for all n that are not prime, so that
the algebra of multiplicative H-invariants of A_{n-1} has a non-trivial Picard
group.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph