Noncommutative projective geometry

In mathematics, noncommutative projective geometry is a noncommutative analog of projective geometry in the setting of noncommutative algebraic geometry.

Examples

• The quantum plane, the most basic example, is the quotient ring of the free ring:

$k\langle x,y\rangle /(yx-qxy)$

• More generally, the quantum polynomial ring is the quotient ring:

$k\langle x_{1},\dots ,x_{n}\rangle /(x_{i}x_{j}-q_{ij}x_{j}x_{i})$

References

• Ajitabh, Kaushal (1994), Modules over regular algebras and quantum planes (PDF) (Ph.D. thesis)
• Artin M.: Geometry of quantum planes, Contemporary Mathematicsv. 124 (1992).
• Rogalski, D (2014). "An introduction to Noncommutative Projective Geometry". arXiv:1403.3065. A bot will complete this citation soon. Click here to jump the queue

See also

• elliptic algebra
• Calabi–Yau algebra