A quantum symmetric pair consists of a quantum group U $\mathbf {U} $ and its coideal
subalgebra U ς ı ${\mathbf {U}}^{\imath} _ {\bm {\varsigma}} $ with parameters ς $\bm …

In this paper, we consider the singularity category D sg (mod A) and the Z-graded singularity
category D sg (mod ZA) for a Gorenstein monomial algebra A. Firstly, for a positively graded …

We investigate the (separated) monomorphism category mono (Q, Λ) $\operatorname
{mono}(Q,\Lambda) $ of a quiver over an Artin algebra Λ $\Lambda $. We show that there …

Happel constructed a fully faithful functor H: D b (mod Λ)→ mod _ ZT (Λ) for a finite
dimensional algebra Λ. He also showed that this functor H gives an equivalence precisely …

A quantum symmetric pair consists of a quantum group $\mathbf U $ and its coideal
subalgebra ${\mathbf U}^{\imath} _ {\boldsymbol {\varsigma}} $ with parameters …

We study tilting objects of the stable category CM _ ZA of graded Cohen-Macaulay modules
over a finite dimensional graded Iwanaga-Gorenstein algebra A. We first show that if there …

We show that for the path algebra A of an acyclic quiver, the singularity category of the
derived category D b (mod A) is triangle equivalent to the derived category of the functor …

This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be
divided into four parts: The first part is an introduction to the theory of monomorphism …

An Artin algebra Λ is said to be of finite Cohen–Macaulay type if, up to isomorphism, there
are only finitely many indecomposable modules in G (Λ), the full subcategory of modΛ …

In this paper, we consider the singularity category $ D_ {sg}(\mod A) $ and the $\mathbb {Z}
$-graded singularity category $ D_ {sg}(\mod^{\mathbb Z} A) $ for a Gorenstein monomial …