15 citations · 54 across the 15 of their papers we have counts for
15 papers
A categorical characterization of quantum projective -spaces
Izuru Mori, Adam Nyman
In this paper, we study a generalization of the notion of AS-regularity for connected -algebras. Our main result is a characterization of those categories equivalent to…
Clifford quadratic complete intersections
Haigang Hu, Izuru Mori
In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural…
Noncommutative conics in Calabi-Yau quantum projective planes
Haigang Hu, Masaki Matsuno, Izuru Mori
In noncommutative algebraic geometry, noncommutative quadric hypersurfaces are major objects of study. In this paper, we focus on studying noncommutative conics $\operatorname{Proj…
Quantum Projective Planes Finite over their Centers
Ayako Itaba, Izuru Mori
For a -dimensional quantum polynomial algebra , Artin-Tate-Van den Bergh showed that is finite over its center if and only if . Moreover, Art…
Local duality for connected Z-algebras
Izuru Mori, Adam Nyman
We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of…
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'…
Moduli of noncommutative Hirzebruch surfaces
Izuru Mori, Shinnosuke Okawa, Kazushi Ueda
We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank…
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…
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…
m-Koszul Artin-Schelter regular algebras
Izuru Mori, S. Paul Smith
This paper studies the homological determinants and Nakayama automorphisms of not-necessarily-noetherian -Koszul twisted Calabi-Yau or, equivalently, -Koszul Artin-Schelter r…
The Classification of 3-Calabi-Yau algebras with 3 generators and 3 quadratic relations
Izuru Mori, S. Paul Smith
Let be an algebraically closed field of characteristic not 2 or 3, a 3-dimensional vector space over , a 3-dimensional subspace of , and the qu…
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…
The Grothendieck Group of a Quantum Projective Space Bundle
I. Mori, S. Paul Smith
We compute the Grothendieck group K_0 of non-commutative analogues of quantum projective space bundles. Our results specialize to give the Grothendieck groups of non-commutative an…