Representation Theory of Lie algebras of vector fields on smooth algebraic manifolds
Identities in (non) associative algebras and related themes.
| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF - Brazil
[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 427, p. 226-251, APR 1 2015. |
| Web of Science Citations: | 1 |
| Abstract | |
Let K be a field of characteristic 0 and let W-1 be the Lie algebra of the derivations of the polynomial ring K{[}t]. The algebra W-1 admits a natural Z-grading. We describe the graded identities of W-1 for this grading. It turns out that all these Z-graded identities are consequences of a collection of polynomials of degree 1, 2 and 3 and that they do not admit a finite basis. Recall that the ``ordinary{''} (non-graded) identities of W-1 coincide with the identities of the Lie algebra of the vector fields on the line and it is a long-standing open problem to find a basis for these identities. We hope that our paper might be a step to solving this problem. (c) 2015 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 14/09310-5 - Algebraic structures and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Projects - Thematic Grants |