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pro vyhledávání: '"Ueyama, Kenta"'
Autor:
Ueyama, Kenta
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G2, Pp 521-534 (2023)
For a skew version of a graded $(A_\infty )$ hypersurface singularity $A$, we study the stable category of graded maximal Cohen-Macaulay modules over $A$. As a consequence, we see that $A$ has countably infinite Cohen–Macaulay representation type a
Externí odkaz:
https://doaj.org/article/d197237df4674db1bc49988018f5bf5c
Autor:
Higashitani, Akihiro, Ueyama, Kenta
We introduce an operation on skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ called switching, and also define a class of skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ referred to as modular Eulerian matrices. We then show that th
Externí odkaz:
http://arxiv.org/abs/2409.10904
The existence of a tilting or silting object is an important feature for an algebraic triangulated category since it gives an equivalence with the derived category of a ring. By applying tilting theory, we study Cohen-Macaulay representations of $\ma
Externí odkaz:
http://arxiv.org/abs/2404.05925
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-cocycle twists of certain bialgebras. We then outline the classification a
Externí odkaz:
http://arxiv.org/abs/2211.15885
Autor:
Ueyama, Kenta
For a skew version of a graded $(A_\infty)$ hypersurface singularity $A$, we study the stable category of graded maximal Cohen-Macaulay modules over $A$. As a consequence, we see that $A$ has countably infinite Cohen-Macaulay representation type and
Externí odkaz:
http://arxiv.org/abs/2204.05501
Autor:
He, Ji-Wei, Ueyama, Kenta
We introduce the notion of the twisted Segre product $A\circ_\psi B$ of $\mathbb Z$-graded algebras $A$ and $B$ with respect to a twisting map $\psi$. It is proved that if $A$ and $B$ are noetherian Koszul Artin-Schelter regular algebras and $\psi$ i
Externí odkaz:
http://arxiv.org/abs/2111.04245
Autor:
Higashitani, Akihiro, Ueyama, Kenta
The noncommutative projective scheme $\operatorname{\mathsf{Proj_{nc}}} S$ of a $(\pm 1)$-skew polynomial algebra $S$ in $n$ variables is considered to be a $(\pm 1)$-skew projective space of dimension $n-1$. In this paper, using combinatorial method
Externí odkaz:
http://arxiv.org/abs/2107.12927
Autor:
Ueyama, Kenta
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 of this result. Namely, we show that if $S$ is a standard graded $(\p
Externí odkaz:
http://arxiv.org/abs/2008.02255
Autor:
Higashitani, Akihiro, Ueyama, Kenta
In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let $S$ be a graded ($\pm 1$)-skew polynomial algebra in $n$ variables of degree $1$ and $f =x_1^2 + \cdots +x_n^2 \in S$. We
Externí odkaz:
http://arxiv.org/abs/1910.10612
Autor:
Mori, Izuru, Ueyama, Kenta
Publikováno v:
Alg. Number Th. 16 (2022) 467-504
Noncommutative hypersurfaces, in particular, noncommutative quadric hypersurfaces are major objects of study in noncommutative algebraic geometry. In the commutative case, Kn\"orrer's periodicity theorem is a powerful tool to study Cohen-Macaulay rep
Externí odkaz:
http://arxiv.org/abs/1905.12266