Zobrazeno 1 - 10
of 69
pro vyhledávání: '"Brooksbank, Peter A."'
A tensor consists of data, $t$, equipped with a multilinear product $\langle t|u_1,\ldots, u_{\ell}\rangle$, called a tensor contraction. Each vector $u_a$ comes from a space $U_a$ called an axis (or mode), the output $\langle t|u_1,\ldots, u_{\ell}\
Externí odkaz:
http://arxiv.org/abs/2408.17425
Publikováno v:
J. Algebra 604 (2022), 790--807
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable we give a
Externí odkaz:
http://arxiv.org/abs/2005.04046
Autor:
Brooksbank, Peter A.
We determine the ranks of string C-group representations of the groups ${\rm PSp}(4,\mathbb{F}_q)\cong\Omega(5,\mathbb{F}_q)$, and comment on those of higher-dimensional symplectic and orthogonal groups.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/1912.05512
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show how to combi
Externí odkaz:
http://arxiv.org/abs/1905.02518
Autor:
Brooksbank, Peter A., Leemans, Dimitri
We show that a rank reduction technique for string C-group representations first used for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on $d$-dimensional
Externí odkaz:
http://arxiv.org/abs/1812.01055
Publikováno v:
J. Algebra, 2020, 545, 43--63
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner similar to t
Externí odkaz:
http://arxiv.org/abs/1812.00275
Publikováno v:
In Journal of Algebra 15 August 2022 604:790-807
We show that for all integers $m\geq 2$, and all integers $k\geq 2$, the orthogonal groups $\Orth^{\pm}(2m,\Fk)$ act on abstract regular polytopes of rank $2m$, and the symplectic groups $\Sp(2m,\Fk)$ act on abstract regular polytopes of rank $2m+1$.
Externí odkaz:
http://arxiv.org/abs/1709.02219
Publikováno v:
Trans. Amer. Math. Soc. 2019
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramat
Externí odkaz:
http://arxiv.org/abs/1708.08873
Publikováno v:
J. Algebra, 2017 (473) 545--590
Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited to studying local properties of general finite groups. We also report o
Externí odkaz:
http://arxiv.org/abs/1508.03033