2021/07/20 by V. V. Bavula, Bavula, V. V.
Mathematics · #13N10 #16D60 #16P90 #16S32 #16U20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2107.09401
openalex publication_date 2021/07/20 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28
Let Ł(f) = K[x][y; f(d)/(dx) ] be an Ore extension of a polynomial algebra K[x] over a field K of characteristic zero where f∈ K[x]. For a given polynomial f, the automorphism group of the algebra Ł(f) is explicitly described. The polynomial case Ł(0) = K[x,y] and the case of the Weyl algebra A1= K[x][y; (d)/(dx) ] were done done by Jung (1942) and van der Kulk (1953), and Dixmier (1968), respectively. In 1997, Alev and Dumas proved that the algebras Ł(f) and Ł(g) are isomorphic iff g(x) = łf(αx+β) for some ł, α∈ K\backslash \ 0\ and β∈ K. In 2015, Benkart, Lopes and Ondrus gave a complete description of the set of automorphism groups of algebras Ł(f). In this paper we complete the picture, i.e. \em given the polynomial f we have the explicit description of the automorphism group of Ł(f).