Archiv der Mathematik

, Volume 75, Issue 2, pp 98–112 | Cite as

Modules over the algebra of the noncommutative equation yx = 1

  • L. Gerritzen


In this paper the associative algebra A generated by two elements x, y with defining relation y x = 1 is considered. An explicit description of the system of right ideals of A is obtained. Also a structure theorem for right modules over A in terms of extensions of modules is given. One can view A as the algebra of a non-commutative torus and one can construct a non-commutative projective line by adjoining points at infinity. Results about the Lie algebra of derivations of A and the group of automorphisms of A are derived.


Associative Algebra Explicit Description Projective Line Structure Theorem 
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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • L. Gerritzen
    • 1
  1. 1.Ruhr-Universität Bochum, Fakultät und Institut für Mathematik, Gebäude NA 2/33, Universitätsstr. 150, D-44780 BochumDE

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