Regular representations of finite-dimensional separable semisimple algebras and Grbner bases
Let be a semisimple n-dimensional commutative algebra over a field . It is easy to see that, given a basis of , the transposes of the matrices over that represent regularly with respect to can be simultaneously diagonalized over many fields. Using the multiplication table of the algebra we construct an ideal of given in terms of a Grbner basis of the ideal with respect to a total degree lexicographic monomial ordering and show that is isomorphic to . We will then use Grbner basis properties to prove the properties of the algebra.
regular representation semisimple algebras grbner bases