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pro vyhledávání: '"Snowden, Andrew"'
Autor:
Snowden, Andrew
Let $\mathfrak{C}$ be a symmetric tensor category and let $A$ be an Azumaya algebra in $\mathfrak{C}$. Assuming a certain invariant $\eta(A) \in \mathrm{Pic}(\mathfrak{C})[2]$ vanishes, and fixing a certain choice of signs, we show that there is a un
Externí odkaz:
http://arxiv.org/abs/2408.00233
Autor:
Harman, Nate, Snowden, Andrew
A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we generalize
Externí odkaz:
http://arxiv.org/abs/2407.19132
Autor:
Nekrasov, Ilia, Snowden, Andrew
In recent work, Harman and Snowden introduced a notion of measure on a Fra\"iss\'e class $\mathfrak{F}$, and showed how such measures lead to interesting tensor categories. Constructing and classifying measures is a difficult problem, and so far only
Externí odkaz:
http://arxiv.org/abs/2407.19131
Autor:
Lampert, Amichai, Snowden, Andrew
Let $K$ be a Birch field, that is, a field for which every diagonal form of odd degree in sufficiently many variables admits a non-zero solution; for example, $K$ could be the field of rational numbers. Let $f_1, \ldots, f_r$ be homogeneous forms of
Externí odkaz:
http://arxiv.org/abs/2406.18498
A $\mathbf{GL}$-variety is a (typically infinite dimensional) variety modeled on the polynomial representation theory of the general linear group. In previous work, we studied these varieties in characteristic 0. In this paper, we obtain results in p
Externí odkaz:
http://arxiv.org/abs/2406.07415
Autor:
Snowden, Andrew
In recent work with Harman, we introduced a notion of measure on a class of finite relational structures. In this note, we consider measures on the class of permutations, i.e., finite sets with two total orders. Using a method of Nekrasov, we show th
Externí odkaz:
http://arxiv.org/abs/2404.08775
Autor:
Snowden, Andrew
Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure. In this pa
Externí odkaz:
http://arxiv.org/abs/2403.16267
Let $k$ be a Brauer field, that is, a field over which every diagonal form in sufficiently many variables has a nonzero solution; for instance, $k$ could be an imaginary quadratic number field. Brauer proved that if $f_1, \ldots, f_r$ are homogeneous
Externí odkaz:
http://arxiv.org/abs/2401.02067
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction is based o
Externí odkaz:
http://arxiv.org/abs/2308.06660
Autor:
Snowden, Andrew
In previous work with Harman, we introduced a new class of representations for an oligomorphic group $G$, depending on an auxiliary piece of data called a measure. In this paper, we look at this theory when $G$ is the symmetry group of the Cantor set
Externí odkaz:
http://arxiv.org/abs/2308.06648