Constructing endomorphism rings via duals

  • Authors:

  • Edward L. Green;Lenwood S. Heath;Craig A. Struble

  • Affiliations:

  • Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA

  • Venue:
  • ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
  • Year:
  • 2000

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Abstract

We present a new deterministic algorithm for constructing endomorphism rings of a finite dimensional module M, given via a vertex projective presentation, over finite dimensional quotients of path algebras. We use the theory of right Gröbner basis to encode M and to construct appropriate systems of equations for finding the endomorphism ring of M. The algorithm is implemented in the computer algebra system GAP and is included in HOPF, a computational package for noncommutative algebra. We compare the performance of our implementation with implementations of existing algorithms for computing endomorphism rings.