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Modules Over Elliptic Algebras and Quantum Planes
Author(s) -
Ajitabh Kaushal
Publication year - 1996
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-72.3.567
Subject(s) - mathematics , projective plane , pure mathematics , dimension (graph theory) , elliptic curve , quantum , point (geometry) , commutative property , plane (geometry) , algebra over a field , geometry , physics , quantum mechanics , correlation
This is a study of modules over elliptic algebras, especially modules of Gelfand‐Kirillov dimension 2. An elliptic algebra A is associated with a certain automorphism of a one‐dimensional scheme E , generally an elliptic curve, and every elliptic algebra defines a ‘non‐commutative projective plane’ proj‐ A , sometimes called a quantum plane. Therefore, the study of modules translates into an interplay between the geometries of E and of quantum planes. The relation to geometry is studied by looking at ‘the points of a given module M ’ and corresponding ‘incidence relations’ (a point p of E is said to be a point of M if there is a non‐zero map from M to the corresponding point module N p ).