Noncommutative plane curves

2004/05/18 by S. Jøndrup, Olav Arnfinn Laudal, O. A. Laudal +5 · 1 citation
Mathematics · #14A22 #14H50 #14R #16D60 #16G30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14A22 #msc:14H50 #msc:14R #msc:16D60 #msc:16G30

paper · pdf · doi:10.48550/arxiv.math/0405350

31 pages

arxiv created 2004/05/18 · openalex publication_date 2004/05/18 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study noncommutative plane curves, i.e. non-commutative k-algebras for which the 1-dimensional simple modules form a plane curve. We study extensions of simple modules and we try to enlighten the completion problem, i.e. understanding the connection between simple modules of different dimension.

Citations

• The invariant theory of n × n matrices
• Finite dimensional representations of algebras

Cited by

• A quantum-trace determinantal formula for matrix commutators, and applications

Related

• Noncommutative projective geometry
• Noncommutative curves and noncommutative surfaces
• Noncommutative curves of genus zero: related to finite dimensional algebras
• An introduction to Noncommutative Projective Geometry
• Introduction into Noncommutative Algebra, Volume 2