Automorphisms of elliptic Poisson algebras
We describe the automorphism groups of elliptic Poisson algebras on polynomial algebras in three variables and give an explicit set of generators and defining relations for this group.
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arXiv subjects
Ualbai Umirbaev
Publications and source records attributed to Ualbai Umirbaev.
Automorphisms and derivations of free Poisson algebras in two variables
Let P be a free Poisson algebra in two variables over a field of characteristic zero. We prove that the automorphisms of P are tame and that the locally nilpotent derivations of P are triangulable.
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Defining relations for automorphism groups of free algebras
We describe a set of defining relations for automorphism groups of finitely generated free algebras of Nielsen-Schreier varieties. In particular, this gives a representation of the automorphism groups of free Lie algebras by generators and defining relations.
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Defining relations of the tame automorphism group of polynomial algebras in three variables
We describe a set of defining relations of the tame automorphism group TA_3(F) of the polynomial algebra F[x_1,x_2,x_3] in variables x_1,x_2,x_3 over an arbitrary field F of characteristic 0.
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The Anick automorphism of free associative algebras
We prove that the well-known Anick automorphism of the free associative algebra F over an arbitrary field F of characteristic 0 is wild.
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