7 citations · 13 across the 15 of their papers we have counts for
18 papers
Noncommutative tensor triangular geometry: modules, bimodules, and unipotent Hopf algebras
Øyvind Solberg, Kent B. Vashaw, Sarah Witherspoon
We initiate a program aimed at classifying thick ideals, Balmer spectra, and submodule categories of various stable categories of bimodules and modules for finite dimensional selfi…
Non-negligible summands in tensor powers of some modular representations of finite -groups
Kent B. Vashaw, Justin Zhang
Let be a prime, be a finite -group and be an algebraically closed field of characteristic . Dave Benson has conjectured that if and is an odd-dime…
Quantum-symmetric equivalence for superpotential algebras
Hongdi Huang, Van C. Nguyen, Kent B. Vashaw +2
We study superpotential algebras by introducing the notion of quantum-symmetric equivalence defined relatively to two fixed Hopf coactions. This concept relies on the non-vanishing…
The homological spectrum for monoidal triangulated categories
Daniel K. Nakano, Kent B. Vashaw, Milen T. Yakimov
The authors develop a notion of homological prime spectrum for an arbitrary monoidal triangulated category, . Unlike the symmetric case due to Balmer, the homological…
Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry
Peter Goetz, Ellen E. Kirkman, W. Frank Moore +1
Let be a group coacting on an Artin-Schelter regular algebra homogeneously and inner-faithfully. When the identity component is also Artin-Schelter regular, providing…
Formal extension of noncommutative tensor-triangular support varieties
Merrick Cai, Kent B. Vashaw
Given a support variety theory defined on the compact part of a monoidal triangulated category, we define an extension to the non-compact part following the blueprint of Benson--Ca…
Quantum-symmetric equivalence is a graded Morita invariant
Hongdi Huang, Van C. Nguyen, Padmini Veerapen +2
We show that if two -homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalen…
A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories
Daniel K. Nakano, Kent B. Vashaw, Milen T. Yakimov
In this paper the authors prove fundamental decomposition theorems pertaining to the internal structure of monoidal triangulated categories (MCs). The tensor structure of an M$Δ…
Group actions on monoidal triangulated categories and Balmer spectra
Hongdi Huang, Kent B. Vashaw
Let be a group acting on a left or right rigid monoidal triangulated category which has a Noetherian Balmer spectrum. We prove that the Balmer spectrum of the cro…
On the decomposition of tensor products of monomial modules for finite 2-groups
George Cao, Kent B. Vashaw
Dave Benson conjectured in 2020 that if is a finite -group and is an odd-dimensional indecomposable representation of over an algebraically closed field of c…
Twisting Manin's universal quantum groups and comodule algebras
Hongdi Huang, Van C. Nguyen, Charlotte Ure +3
We introduce the notion of quantum-symmetric equivalence of two connected graded algebras, based on Morita-Takeuchi equivalences of their universal quantum groups, in the sense of…
On the spectrum and support theory of a finite tensor category
Daniel K. Nakano, Kent B. Vashaw, Milen T. Yakimov
Finite tensor categories (FTCs) are important generalizations of the categories of finite dimensional modules of finite dimensional Hopf algebras, which play a key role in…
A cogroupoid associated to preregular forms
Hongdi Huang, Van C. Nguyen, Charlotte Ure +3
We construct a family of cogroupoids associated to preregular forms and recover the Morita-Takeuchi equivalence for Artin-Schelter regular algebras of dimension two, observed by Ra…
Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation
Hongdi Huang, Van C. Nguyen, Charlotte Ure +3
Let be a Hopf algebra that is -graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of to be a Zhang twist of . In particular, we intr…
Balmer spectra and Drinfeld centers
Kent B. Vashaw
The Balmer spectrum of a monoidal triangulated category is an important geometric construction which is closely related to the problem of classifying thick tensor ideals. We prove…
Noncommutative tensor triangular geometry and the tensor product property for support maps
Daniel K. Nakano, Kent B. Vashaw, Milen T. Yakimov
The problem of whether the cohomological support map of a finite dimensional Hopf algebra has the tensor product property has attracted a lot of attention following the earlier dev…
Noncommutative tensor triangular geometry
Daniel K. Nakano, Kent B. Vashaw, Milen T. Yakimov
We develop a general noncommutative version of Balmer's tensor triangular geometry that is applicable to arbitrary monoidal triangulated categories (MCs). Insight from noncommut…
Prime spectra of abelian 2-categories and categorifications of Richardson varieties
Kent Vashaw, Milen Yakimov
We describe a general framework for prime, completely prime, semiprime, and primitive ideals of an abelian 2-category. This provides a noncommutative version of Balmer's prime spec…