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On the Quantum Spaces of Some Quadratic Regular Algebras of Global Dimension Four
(2016-05-10)
A quantum $\mathbb{P}^3$ is a noncommutative analogue of a polynomial ring on four variables, and, herein, it is taken to be a regular algebra of global dimension four. It is well known that if a generic quadratic quantum ...
SOME QUADRATIC QUANTUM P³s WITH A LINEAR ONE-DIMENSIONAL LINE SCHEME
(2021-05-20)
It is believed that quadratic Artin-Shelter regular (AS-regular) algebras of global dimension four (sometimes called quadratic quantum P3s can be classified using a geometry similar to that developed in the 1980’s by ...
Projective Geometry Associated to some Quadratic, Regular Algebras of Global Dimension Four
(2018-05-02)
The attempted classification of regular algebras of global dimension four, so-called quantum P³s, has been a driving force for modern research in noncommutative algebra. Inspired by the work of Artin, Tate, and Van den ...