| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Carleton Univ, Sch Math & Stat, Ottawa, ON - Canada
[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | COMMUNICATIONS IN ALGEBRA; v. 46, n. 8, p. 3413-3429, 2018. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 15/05859-5 - Lie algebras of vector fields on algebraic varieties |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 14/09310-5 - Algebraic structures and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Projects - Thematic Grants |