AFRICA MATHEMATICS ANNALS

Mathematics Subject Classification: (MSC 2010) 16S32
Key words : First Weyl algebra with non-zero characteristic, center of the first algebra

Abstract:

Let A₁(k) = k[x,y] with the relation yx - xy = 1, be the first Weyl Algebra over a nonzero characteristic field k. Up to now, with the first authors who worked on Weyl Algebras, we have not come across specific studies on invariant elements of A₁(k). This is the reason why, we decided to study these singular elements by proving that their set is the subalgebra k[x^py^p] of the center k[x^p,y^p] of A₁(k). This demonstrates that invariant elements in nonzero characteristic field are not limited to scalars as it is the case of zero characteristic field. And the results may help in resolving some complex equations related to the determination of the centralizers and establishing other properties in Weyl Algebras.