Automorphism groups of Witt algebras

2015/02/05 by Jianzhi Han, Han, Jianzhi, Yucai Su +1
Mathematics · #16S50 #17B40 #Commutative Algebra (math.AC) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AC #math.QA #msc:16S50 #msc:17B40

paper · pdf · doi:10.48550/arxiv.1502.01441

arxiv created 2015/02/05 · arxiv updated 2015/02/06

Abstract

The automorphism groups \rm Aut A_n and \rm Aut W_n of the polynomial algebra A_n=C[x₁,x₂,⋯, x_n] and the rank n Witt algebra W_n=\rm Der A_n are studied in this paper. It is well-known that \rm Aut A_n for n≥3 and \rm Aut W_n for n≥2 are open. In the present paper, by characterizing the semigroup \rm End W_n∖\0\ of nonzero endomorphisms of W_n via the semigroup of the so-called Jacobi tuples, we establish an isomorphism between \rm Aut A_n and \rm Aut W_n for any positive integer n. In particular, this enables us to work out the automorphism group \rm Aut W₂ of W₂.

Related

• The groups of automorphisms of the Witt W_n and Virasoro Lie algebras
• Witt vector rings and quotients of monoid algebras
• Borel subalgebras of the Witt algebra W₁
• The group of automorphisms of the Jacobian algebra \mA_n
• Polynomial representations of the Witt Lie algebra