Details:
Title  Regular representations of finitedimensional separable semisimple algebras and Gröbner bases  Author(s)  Edgar Martı́nezMoro  Type  Article in Journal  Abstract  Let A be a semisimple ndimensional commutative algebra over a field F. It is easy to see that, given a basis B of A, the transposes of the matrices over F that represent a∈A regularly with respect to B can be simultaneously diagonalized over many fields. Using the multiplication table of the algebra we construct an ideal I of F[x_1,…,x_n] given in terms of a Gröbner basis of the ideal I with respect to a total degree lexicographic monomial ordering and show that A is isomorphic to F[x_1,…,x_n]/I. We will then use Gröbner basis properties to prove the properties of the algebra.  Keywords  Gröbner bases, Regular representation, Semisimple algebras  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717103001238 
Language  English  Journal  Journal of Symbolic Computation  Volume  37  Number  5  Pages  575  587  Year  2004  Edition  0  Translation 
No  Refereed 
No 
