David J. Benson
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View article: Utilization of Artificial Intelligence Coupled with a High-Throughput, High-Content Platform in the Exploration of Neurodevelopmental Toxicity of Individual and Combined PFAS
Utilization of Artificial Intelligence Coupled with a High-Throughput, High-Content Platform in the Exploration of Neurodevelopmental Toxicity of Individual and Combined PFAS Open
Per- and polyfluoroalkyl substances (PFAS) are synthetic chemicals used in various products, such as firefighting foams and non-stick cookware, due to their resistance to heat and degradation. However, these same properties make them persi…
View article: Integrated Hydro-terrestrial Modeling 2.0: Progress and Path Forward on Building a National Capability
Integrated Hydro-terrestrial Modeling 2.0: Progress and Path Forward on Building a National Capability Open
It is the role of the U.S. federal government and its supporting agencies, including academia and future scientists, to ensure that its people have sustained and equitable freshwater services, as well as the critical knowledge necessary to…
View article: Modules with finitely generated cohomology
Modules with finitely generated cohomology Open
Peer reviewed
View article: The cohomology of the nilCoxeter algebra
The cohomology of the nilCoxeter algebra Open
The nilCoxeter algebra $\mathcal{N}S_n$ of the symmetric group $S_n$ is the algebra over $\mathbb{Z}$ with generators $Y_i$ ($1\leqslant i\leqslant n-1$), satisfying the braid relations $Y_iY_{i+1}Y_i=Y_{i+1}Y_iY_{i+1}$, $Y_iY_j=Y_jY_i$ ($…
View article: Projective Modules and Cohomology for Integral Basic Algebras
Projective Modules and Cohomology for Integral Basic Algebras Open
Algebras defined over fields of characteristic zero and positive characteristic usually do not behave the same way. However, for certain algebras, for example the group algebras, they behave the same way as the characteristic zero case at …
View article: Modules with finitely generated cohomology, and singularities of C⁎BG
Modules with finitely generated cohomology, and singularities of C⁎BG Open
Peer reviewed
View article: Matrices for finite group representations that respect Galois automorphisms
Matrices for finite group representations that respect Galois automorphisms Open
We are given a finite group H , an automorphism $$\tau $$ of H of order r , a Galois extension L / K of fields of characteristic zero with cyclic Galois group $$\langle \sigma \rangle $$ of order r , and an absolutely irreducible re…
View article: Fibrewise stratification of group representations
Fibrewise stratification of group representations Open
Given a finite cocommutative Hopf algebra over a commutative regular ring , the lattice of localising tensor ideals of the stable category of Gorenstein projective -modules is described in terms of the corresponding lattices for the fibre…
View article: Using Isogeometric Analysis to Model Cylindrical Shock Hydrodynamics
Using Isogeometric Analysis to Model Cylindrical Shock Hydrodynamics Open
View article: The socle of the group algebra of a finite p-group
The socle of the group algebra of a finite p-group Open
Let G be a finite p-group, and α an automorphism of the group algebra FpG. Then α fixes the socle of FpG pointwise. More generally, if k is a field of characteristic p, and α is a k-algebra automorphism of kG, then α induces a linear actio…
View article: Modules with finitely generated cohomology
Modules with finitely generated cohomology Open
Let $G$ be a finite group and $\mathsf{k}$ a field of characteristic $p$. It is conjectured in a paper of the first author and John Greenlees that the thick subcategory of the stable module category StMod$(\mathsf{k}G)$ consisting of modul…
View article: Matrices for finite group representations that respect Galois automorphisms
Matrices for finite group representations that respect Galois automorphisms Open
We are given a finite group $H$, an automorphism $τ$ of $H$ of order $r$, a Galois extension $L/K$ of fields of characteristic zero with cyclic Galois group $\langleσ\rangle$ of order $r$, and an absolutely irreducible representation $ρ\co…
View article: Issue Information
Issue Information Open
representations) c.W. eAton (Finite groups and representation theory) b.
View article: Centralisers of finite groups in locally finite simple groups
Centralisers of finite groups in locally finite simple groups Open
We answer in the negative a question of Hartley about representations of finite groups, by constructing examples of finite simple groups with arbitrarily large representations whose endomorphism ring consists of just the scalars. We show a…
View article: Modules with finitely generated cohomology, and singularities of $C^*BG$
Modules with finitely generated cohomology, and singularities of $C^*BG$ Open
Let $G$ be a finite group and $k$ a field of characteristic $p$. We conjecture that if $M$ is a $kG$-module with $H^*(G,M)$ finitely generated as a module over $H^*(G,k)$ then as an element of the stable module category $\mathsf{StMod}(kG)…
View article: Hochschild cohomology of symmetric groups and generating functions, II
Hochschild cohomology of symmetric groups and generating functions, II Open
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of the symmetric groups. We show that the first Hochschild cohomology of a positive defect b…
View article: The socle of the group algebra of a finite $p$-group
The socle of the group algebra of a finite $p$-group Open
Let $G$ be a finite $p$-group, and $α$ an automorphism of the group algebra ${\mathbb F}_pG$. Then $α$ fixes the socle of ${\mathbb F}_pG$ pointwise. More generally, if $k$ is a field of characteristic $p$, and $α$ is a $k$-algebra automor…
View article: Hochschild cohomology of symmetric groups and generating functions,II
Hochschild cohomology of symmetric groups and generating functions,II Open
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of the symmetric groups. We show that the first Hochschild cohomology of a positive defect b…
Structure of blocks with normal defect and abelian inertial quotient Open
View article: Formality of cochains on BG$BG$
Formality of cochains on BG$BG$ Open
Let be a compact Lie group with maximal torus . If is invertible in the field , then the algebra of cochains is formal as an algebra, or equivalently as a differential graded algebra.
View article: Classifying spaces of finite groups of tame representation type
Classifying spaces of finite groups of tame representation type Open
Thanks to the work of Karin Erdmann, we know a great deal about the representation theory of blocks of finite groups with tame representation type. Our purpose here is to examine the $p$-completed classifying spaces of these blocks and the…
View article: Centralisers of finite groups in locally finite simple groups
Centralisers of finite groups in locally finite simple groups Open
We answer in the negative a question of Hartley about representations of finite groups, by constructing examples of finite simple groups with arbitrarily large representations whose endomorphism ring consists of just the scalars. We show a…
View article: Formality of cochains on BG
Formality of cochains on BG Open
Let $G$ be a compact Lie group with maximal torus $T$. If $|N_G(T)/T|$ is invertible in the field $k$ then the algebra of cochains $C^*(BG;k)$ is formal as an $A_\infty$ algebra, or equivalently as a DG algebra.
View article: Issue Information
Issue Information Open
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.The Journal is known for welcoming contrib…
View article: Hochschild cohomology of symmetric groups in low degrees
Hochschild cohomology of symmetric groups in low degrees Open
We compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the Hochs…
View article: Structure of blocks with normal defect and abelian $p'$ inertial quotient
Structure of blocks with normal defect and abelian $p'$ inertial quotient Open
Let $k$ be an algebraically closed field of prime characteristic $p$. Let $kGe$ be a block of a group algebra of a finite group $G$, with normal defect group $P$ and abelian $p'$ inertial quotient $L$. Then we show that $kGe$ is a matrix a…
View article: On cohomology in symmetric tensor categories in prime characteristic
On cohomology in symmetric tensor categories in prime characteristic Open
We describe graded commutative Gorenstein algebras ${\mathcal E}_n(p)$ over a field of characteristic $p$, and we conjecture that $\mathrm{Ext}^\bullet_{\mathsf{Ver}_{p^{n+1}}}(1,1)\cong{\mathcal E}_{n}(p)$, where $\mathsf{Ver}_{p^{n+1}}$ …
View article: Bounded complexes of permutation modules
Bounded complexes of permutation modules Open
Let be a field of characteristic . For an elementary abelian -group, there exist collections of permutation modules such that if is any exact bounded complex whose terms are sums of copies of modules from the collection, then is contra…
View article: An updated Lagrangian framework for Isogeometric Kirchhoff–Love thin-shell analysis
An updated Lagrangian framework for Isogeometric Kirchhoff–Love thin-shell analysis Open
View article: Modular representation theory and commutative Banach algebras
Modular representation theory and commutative Banach algebras Open
In a recent paper of Benson and Symonds, a new invariant was introduced for modular representations of a finite group. An interpretation was given as a spectral radius with respect to a Banach algebra completion of the representation ring.…