26 citations · 58 across the 19 of their papers we have counts for
20 papers
Iterated Mapping Cones on the Koszul Complex and Their Application to Complete Intersection Rings
Van C. Nguyen, Oana Veliche
Let be a complete intersection local ring, be the Koszul complex on a minimal set of generators of , and be its homology alge…
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…
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…
Tensor Representations for the Drinfeld Double of the Taft Algebra
Georgia Benkart, Rekha Biswal, Ellen Kirkman +2
Over an algebraically closed field of characteristic zero, the Drinfeld double of the Taft algebra that is defined using a primitive th root of unity $q \in \m…
A truncated minimal free resolution of the residue field
Van C. Nguyen, Oana Veliche
In a paper in 1962, Golod proved that the Betti sequence of the residue field of a local ring attains an upper bound given by Serre if and only if the homology algebra of the Koszu…
McKay Matrices for Finite-dimensional Hopf Algebras
Georgia Benkart, Rekha Biswal, Ellen Kirkman +2
For a finite-dimensional Hopf algebra , the McKay matrix of an -module encodes the relations for tensoring the simple -modules with . We prove results about t…
New approaches to finite generation of cohomology rings
Van C. Nguyen, Xingting Wang, Sarah Witherspoon
In support variety theory, representations of a finite dimensional (Hopf) algebra can be studied geometrically by associating any representation of to an algebraic variety…
The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras
Joanna Meinel, Van C. Nguyen, Bregje Pauwels +2
We determine the Gerstenhaber structure on the Hochschild cohomology ring of a class of self-injective special biserial algebras. Each of these algebras is presented as a quotient…
Finite generation of some cohomology rings via twisted tensor product and Anick resolutions
Van C. Nguyen, Xingting Wang, Sarah Witherspoon
Over a field of prime characteristic , we prove that the cohomology rings of some pointed Hopf algebras of dimension are finitely generated. These are Hopf algebras aris…
Dominant dimension and tilting modules
Van C. Nguyen, Idun Reiten, Gordana Todorov +1
We study which algebras have tilting modules that are both generated and cogenerated by projective-injective modules. Crawley-Boevey and Sauter have shown that Auslander algebras h…
Preprojective algebras of tree-type quivers
Van C. Nguyen, Gordana Todorov, Shijie Zhu
Let be a tree-type quiver, its path algebra, and a nonzero element in the field . We construct irreducible morphisms in the Auslander-Reiten quiv…
Pointed -dimensional Hopf algebras in positive characteristic
Van C. Nguyen, Xingting Wang
We classify pointed -dimensional Hopf algebras over any algebraically closed field of prime characteristic . In particular, we focus on the cases when the group $…
Primitive Deformations of Quantum -groups
Van C. Nguyen, Linhong Wang, Xingting Wang
For finite-dimensional Hopf algebras, their classification in characteristic (e.g. over ) has been investigated for decades with many fruitful results, but their st…
Gerstenhaber brackets on Hochschild cohomology of twisted tensor products
Lauren Grimley, Van C. Nguyen, Sarah Witherspoon
We construct the Gerstenhaber bracket on Hochschild cohomology of a twisted tensor product of algebras, and, as examples, compute Gerstenhaber brackets for some quantum complete in…
Finite generation of the cohomology of some skew group algebras
Van C. Nguyen, Sarah Witherspoon
We prove that some skew group algebras have Noetherian cohomology rings, a property inherited from their component parts. The proof is an adaptation of Evens' proof of finite gener…
Finite generation of Tate cohomology of symmetric Hopf algebras
Van C. Nguyen
Let be a finite dimensional symmetric Hopf algebra over a field . We show that there are -modules whose Tate cohomology is not finitely generated over the Tate cohomology…
Classification of connected Hopf algebras of dimension I
Van C. Nguyen, Linhong Wang, Xingting Wang
Let be a prime, be an algebraically closed field of characteristic . In this paper, we provide the classification of connected Hopf algebras of dimension , except t…
The Tate-Hochschild cohomology ring of a group algebra
Van C. Nguyen
We show that the Tate-Hochschild cohomology ring of a finite group algebra is isomorphic to a direct sum of the Tate cohomology rings of the centralizers of conj…
Tate and Tate-Hochschild Cohomology for finite dimensional Hopf Algebras
Van C. Nguyen
Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate-Hochschild cohomology for A and introduce cup products that make them become graded rings.…