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TitleRegular representations of finite-dimensional separable semisimple algebras and Gröbner bases
Author(s) Edgar Martı́nez-Moro
TypeArticle in Journal
AbstractLet A be a semisimple n-dimensional 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.
KeywordsGröbner bases, Regular representation, Semisimple algebras
URL http://www.sciencedirect.com/science/article/pii/S0747717103001238
JournalJournal of Symbolic Computation
Pages575 - 587
Translation No
Refereed No