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Archiv der Mathematik

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

Modules over the algebra of the noncommutative equation yx = 1

  • L. Gerritzen

Abstract.

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.

Keywords

Associative Algebra Explicit Description Projective Line Structure Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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