2009/06/02 by V. V. Bavula, Bavula, V. V.
Mathematics · Physics and Astronomy · #14E07 #14H37 #14R10 #14R15 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.AG #math.RA #msc:14E07 #msc:14H37 #msc:14R10 #msc:14R15
paper · pdf · doi:10.48550/arxiv.0906.0600
13 pages
openalex publication_date 2009/06/02 · arxiv created 2010/04/18 · arxiv updated 2010/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Explicit generators are found for the group G2 of automorphisms of the algebra \mS2 of one-sided inverses of a polynomial algebra in two variables over a field of characteristic zero. Moreover, it is proved that G2≃ S2\ltimes \mT2\ltimes \Z\ltimes ((K^*\ltimes E_∞ (\mS1))\boxtimes\GL_∞ (K)(K^*\ltimes E_∞ (\mS1))) where S2 is the symmetric group, \mT2 is the 2-dimensional torus, E_∞ (\mS1) is the subgroup of \GL_∞ (\mS1) generated by the elementary matrices. In the proof, we use and prove several results on the index of operators, and the final argument in the proof is the fact that \rm K1 (\mS1) ≃ K^* proved in the paper. The algebras \mS1 and \mS2 are noncommutative, non-Noetherian, and not domains. The group of units of the algebra \mS2 is found (it is huge).