15 citations · 45 across the 20 of their papers we have counts for
22 papers
Hypergraphs associated to skew polynomial algebras and surface triangulations
Akihiro Higashitani, Kenta Ueyama
We study the realization problem for point schemes of skew polynomial algebras. We approach this problem combinatorially by translating it into the study of certain -uniform hyp…
Irreducible noncommutative quadrics
Izuru Mori, Kenta Ueyama, Wenchao Wu
In this paper, we study irreducible noncommutative quadrics via noncommutative graded matrix factorizations. We show that the line modules over are described by the…
Trivial extensions of Koszul Artin-Schelter regular algebras
Kenta Ueyama
Let be an -graded Koszul Artin-Schelter regular algebra and let be a graded algebra automorphism of . We study the stable category of graded maximal Cohen-Mac…
A note on even Clifford algebras of skew quadric hypersurfaces
Tomoya Oshio, Kenta Ueyama
Let be a standard graded skew polynomial algebra over an algebraically closed field of characteristic not equal…
On the -polynomials of cyclotomic standard graded commutative algebras
Akihiro Higashitani, Kenta Ueyama
We call a standard graded commutative -algebra cyclotomic if its -polynomial has all its roots on the unit circle in the complex plane. Complete intersections provide typ…
Combinatorics of graded module categories over skew polynomial algebras at roots of unity
Akihiro Higashitani, Kenta Ueyama
We introduce an operation on skew-symmetric matrices over called switching, and also define a class of skew-symmetric matrices over $\mathbb{Z}/\ell\mat…
Cohen-Macaulay representations of Artin-Schelter Gorenstein algebras of dimension one
Osamu Iyama, Yuta Kimura, Kenta Ueyama
Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of…
A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry
Pablo S. Ocal, Kenta Ueyama, Padmini Veerapen
We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocy…
Skew graded hypersurface singularities
Kenta Ueyama
For a skew version of a graded hypersurface singularity , we study the stable category of graded maximal Cohen-Macaulay modules over . As a consequence, we see t…
Twisted Segre products
Ji-Wei He, Kenta Ueyama
We introduce the notion of the twisted Segre product of -graded algebras and with respect to a twisting map . It is proved that if and are…
Combinatorial classification of -skew projective spaces
Akihiro Higashitani, Kenta Ueyama
The noncommutative projective scheme of a -skew polynomial algebra in variables is considered to be a -skew projecti…
Derived categories of skew quadric hypersurfaces
Kenta Ueyama
The existence of a full strong exceptional sequence in the derived category of a smooth quadric hypersurface was proved by Kapranov. In this paper, we present a skew generalization…
Combinatorial study of stable categories of graded Cohen--Macaulay modules over skew quadric hypersurfaces
Akihiro Higashitani, Kenta Ueyama
In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let be a graded ()-skew polynomial algebra in…
Noncommutative Knörrer's periodicity theorem and noncommutative quadric hypersurfaces
Izuru Mori, Kenta Ueyama
Noncommutative hypersurfaces, in particular, noncommutative quadric hypersurfaces are major objects of study in noncommutative algebraic geometry. In the commutative case, Knörrer'…
Hochschild cohomology related to graded down-up algebras with weights
Ayako Itaba, Kenta Ueyama
Let be a graded down-up algebra with and , and let be the Beilinson algebra of . If , then a descriptio…
On Knörrer periodicity for quadric hypersurfaces in skew projective spaces
Kenta Ueyama
We study the structure of the stable category of graded maximal Cohen-Macaulay module over where is a graded ()-skew…
Noncommutative matrix factorizations with an application to skew exterior algebras
Izuru Mori, Kenta Ueyama
Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutati…
A categorical characterization of quantum projective spaces
Izuru Mori, Kenta Ueyama
Let be a finite dimensional algebra of finite global dimension over a field . In this paper, we will characterize a -linear abelian category such that $\math…
The classification of 3-dimensional noetherian cubic Calabi-Yau algebras
Izuru Mori, Kenta Ueyama
It is known that every 3-dimensional noetherian Calabi-Yau algebra generated in degree 1 is isomorphic to a Jacobian algebra of a superpotential. Recently, S. P. Smith and the firs…
Cluster tilting modules and noncommutative projective schemes
Kenta Ueyama
In this paper, we study the relationship between equivalences of noncommutative projective schemes and cluster tilting modules. In particular, we prove the following result. Let $A…
Stable Categories of Graded Maximal Cohen-Macaulay Modules over Noncommutative Quotient Singularities
Izuru Mori, Kenta Ueyama
Tilting objects play a key role in the study of triangulated categories. A famous result due to Iyama and Takahashi asserts that the stable categories of graded maximal Cohen-Macau…
Ample Group Action on AS-regular Algebras and Noncommutative Graded Isolated Singularities
Izuru Mori, Kenta Ueyama
In this paper, we introduce a notion of ampleness of a group action on a right noetherian graded algebra , and show that it is strongly related to the notion of to be…