Lie algebras of vector fields on smooth ane varieties

Autor(es)

Billig, Yuly ^[1] ; Futorny, Vyacheslav ^[2]

Afiliação do(s) autor(es)

^[1] Carleton Univ, Sch Math & Stat, Ottawa, ON - Canada

^[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 46, n. 8, p. 3413-3429, 2018.
• Citações Web of Science: 2

Resumo

We reprove the results of Jordan {[}18] and Siebert {[}30] and show that the Lie algebra of polynomial vector fields on an irreducible ane variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth ane variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered. (AU)

• Processo FAPESP: 15/05859-5 - Álgebras de Lie de campos vetoriais sobre variedades algébricas
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático