Mischenko-Fomenko subalgebras of universal enveloping algebras of simple Lie algebras
Combinatorial aspects of Lie Algebras and of noncomutative algebras
Representations of non-associative algebras and superalgebras
| Full text | |
| Author(s): |
Yasumura, Felipe Yukihide
Total Authors: 1
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| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 674, p. 22-pg., 2023-06-12. |
| Abstract | |
In this paper we construct a graded universal enveloping algebra of a G-graded Lie algebra, where G is not necessarily an abelian group. If the grading group is abelian, then it coincides with the classical construction. We prove the existence and uniqueness of the graded enveloping algebra. As consequences, we prove a graded variant of Witt's Theorem on the universal enveloping algebra of the free Lie algebra, and the graded version of Ado's Theorem, which states that every finite-dimensional Lie algebra admits a faithful finite dimensional representation. Furthermore we investigate if a Lie grading is equivalent to an abelian grading.& COPY; 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |