Corpus ID: 236447586

Combinatorial classification of $(\pm 1)$-skew projective spaces

@inproceedings{Higashitani2021CombinatorialCO,
  title={Combinatorial classification of \$(\pm 1)\$-skew projective spaces},
  author={Akihiro Higashitani and Kenta Ueyama},
  year={2021}
}
The noncommutative projective scheme Projnc S of a (±1)-skew polynomial algebra S in n variables is considered to be a (±1)-skew projective space of dimension n−1. In this paper, using combinatorial methods, we give a classification theorem for (±1)-skew projective spaces. Specifically, among other equivalences, we prove that (±1)-skew projective spaces Projnc S and Projnc S ′ are isomorphic if and only if certain graphs associated to S and S′ are switching (or mutation) equivalent. We also… Expand

References

SHOWING 1-10 OF 31 REFERENCES
Noncommutative Projective Schemes
An analogue of the concept of projective scheme is defined for noncommutative N-graded algebras using the quotient category C of graded right A-modules modulo its full subcategory of torsion modules.Expand
SOME QUANTUM PS WITH FINITELY MANY POINTS
We consider graded Clifford algebras on n generators in the spirit of Artin, Tate and Van den Bergh’s non-commutative algebraic geometry. We give an algorithm for counting the point modules over suchExpand
Embedding a quantum rank three quadric in a quantum P3
We continue the classification, begun in [11], [14] and [12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadricExpand
Some Algebras Associated to Automorphisms of Elliptic Curves
The main object of this paper is to relate a certain type of graded algebra, namely the regular algebras of dimension 3, to automorphisms of elliptic curves. Some of the results were announced inExpand
Regularity of the four dimensional Sklyanin algebra
The notation of a (non-commutative) regular, graded algebra is introduced in (AS). The results of that paper, combined with those in (ATV1, 2), give a complete description of the regular graded ringsExpand
Some quantum P3s with one point
We study a certain 1-parameter family of non-commutative graded regular algebras of global dimension four which were introduced by Vancliff, Van Rompay and Willaert in [12]. Most members of theExpand
Generalizations of graded Clifford algebras and of complete intersections
For decades, the study of graded Clifford algebras has provided a theory where commutative algebraic geometry has dictated the algebraic and homological behavior of a noncommutative algebra. InExpand
Central extensions of three dimensional Artin-Schelter regular algebras
For a 3-dimensional Artin-Schelter-regular algebra A with Hilbert series (1 − t)−3 we study central extensions; that is, graded algebras D with a regular central element z in degree 1, such thatExpand
Regularity of algebras related to the Sklyanin algebra
This paper continues the research of [SS] by finding further examples of (Artin-Schelter) regular rings of dimension four. Unlike the threedimensional case studied in [ATV1, 2], these examples showExpand
Double extension regular algebras of type (14641)
Abstract We construct several families of Artin–Schelter regular algebras of global dimension four using double Ore extension and then prove that all these algebras are strongly noetherian, AuslanderExpand
...
1
2
3
4
...