Browsing by Author "Vancliff, Michaela"
Now showing items 1-7 of 7
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On the Quantum Spaces of Some Quadratic Regular Algebras of Global Dimension Four
Chandler, Richard Gene (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 ... -
Point Modules Over Regular Graded Skew Clifford Algebras
Veerapen, Padmini Pillay (Mathematics, 2013-07-22)In this thesis, I consider point modules over regular graded skew Clifford algebras.First, I define a notion of rank (called μ-rank) on noncommutative quadratic forms. To every (commutative) quadratic form is associated a ... -
Projective Geometry Associated to some Quadratic, Regular Algebras of Global Dimension Four
Tomlin, Derek C. (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 ... -
Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension
Nafari, Manizheh (Mathematics, 2011-10-11)M. Artin, W. Schelter, J. Tate, and M. Van den Bergh introduced the notion of non-commutative regular algebras, and classified regular algebras of global dimension 3 on degree-one generators by using geometry (i.e., point ... -
SOME QUADRATIC QUANTUM P³s WITH A LINEAR ONE-DIMENSIONAL LINE SCHEME
Lim, Ian Christopher; 0000-0001-7834-0994 (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 ... -
Some Quadratic Regular Algebras on Four Generators Wtih A 1-Dimensional Nonreduced Line Scheme
Mastriania, Anthony IV (2019-12-19)In the 1980s, M. Artin, J. Tate, and M. Van den Bergh applied geometric techniques to noncommutative algebras. Their work introduced algebraic concepts called point modules and line modules and an associated geometric ... -
Twisting Systems and some Quantum P³s with Point Scheme a Rank-2 Quadric
Tran, Hung Viet; 0000-0003-4386-3239 (2022-05-18)In 1996, J. J. Zhang introduced the concept of twisting a graded algebra by a twisting system, which generalizes the concept of twisting a graded algebra by an automorphism (the latter concept having been introduced in an ...