Report on a program for solving polynomial equations in non-commuting variables
ACM SIGSAM Bulletin
On the solution of matrix equations, example: Application to invariant equations
Journal of Computational Physics
An extension of Buchberger's algorithm and calculationsin enveloping fields of lie algebras
Journal of Symbolic Computation
Algorithm 628: An algorithm for constructing canonical bases of polynomial ideals
ACM Transactions on Mathematical Software (TOMS)
Groebner Bases for Non-Commutative Polynomial Rings
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
FELIX—an assistant for alebraists
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Constructing Irreducible Representations of Finitely Presented Algebras
Journal of Symbolic Computation
Computer algebra handbook
| Hi-index | 0.01 |
Let a finite presentation be given for an associative, in general non-commutative algebra E, with identity, over a field. We study an algorithm for the construction, from this presentation, of linear, i.e. matrix, representations of this algebra. A set of vector constraints which is given as part of the initial data, determines which particular representation of E is produced. This construction problem for the algebra is solved through a reduction of it to the muchsimpler problem of constructing a Grobner basis for a left module. The price paid for this simplification is that the latter is then infinitely presented. Convergence of the algorithm is proven for all cases where the representation to be found is finite dimensional; which is always the case, for example, when E is finite. Examples are provided, some of which illustrate the close relationship that exists between this method and the Todd-Coxeter coset-enumeration method for group theory.