The Isomorphism Problem for Cyclic Algebras and Its Application

نویسنده

  • TIMO HANKE
چکیده

The isomorphism problem means to decide if two given finitedimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational aspects of representation theory, algebraic geometry and Brauer group theory. The paper presents an algorithm for cyclic algebras that reduces the isomorphism problem to field theory and thus provides a solution if certain field theoretic problems including norm equations can be solved (this is satisfied over number fields). A detailed example is provided which serves to construct an explicit example of a noncrossed product division algebra.

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تاریخ انتشار 2007