37 citations · 43 across the 11 of their papers we have counts for
14 papers
New linear invariants of hypergraphs
Peter A. Brooksbank, Clara R. Chaplin
We introduce a parameterized family of invariants for -uniform hypergraphs. To each -linear transformation we associate a fu…
Categorification of characteristic structures
Peter A. Brooksbank, Heiko Dietrich, Joshua Maglione +2
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing o…
Detecting null patterns in tensor data
Peter A. Brooksbank, Martin D. Kassabov, James B. Wilson
This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in stat…
Isomorphism invariant metrics
P. A. Brooksbank, J. F. Maglione, E. A. O'Brien +1
Within a category , having objects , it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic th…
Tensor Isomorphism by conjugacy of Lie algebras
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
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…
On the ranks of string C-group representations for symplectic and orthogonal groups
Peter A. Brooksbank
We determine the ranks of string C-group representations of the groups , and comment on those of higher-dimensional symplectic and…
Incorporating Weisfeiler-Leman into algorithms for group isomorphism
Peter A. Brooksbank, Joshua A. Grochow, Yinan Li +2
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…
Rank reduction of string C-group representations
Peter A. Brooksbank, Dimitri Leemans
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 ot…
Exact sequences of inner automorphisms of tensors
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
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…
Orthogonal groups in characteristic 2 acting on polytopes of high rank
Peter A. Brooksbank, John T. Ferrara, Dimitri Leemans
We show that for all integers , and all integers , the orthogonal groups $\Orth^{\pm}(2m,\Fk)$ act on abstract regular polytopes of rank , and the symplectic…
Testing isomorphism of graded algebras
Peter A. Brooksbank, E. A. O'Brien, James B. Wilson
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…
A fast isomorphism test for groups of genus 2
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
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 t…
On groups with a class-preserving outer automorphism
Peter A. Brooksbank, Matthew S. Mizuhara
In 1911, Burnside asked whether or not there exist groups that have an outer automorphism which preserves conjugacy classes. Two years later he answered his own question by constru…
Groups acting on tensor products
Peter A. Brooksbank, James B. Wilson
Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and autom…