Homological and combinatorial methods in the theory of Lie Algebras and groups
Abstract groups, pro-p groups and Lie algebras of homological type FPm
Homotopy algebras, symplectic embeddings and non-commutative Gauge Theory
| Full text | |
| Author(s): |
de Mendonca, Luis Augusto
Total Authors: 1
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 529, p. 145-173, JUL 1 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
We study the analogue of Sidki's weak commutativity construction, defined originally for groups, in the category of Lie algebras. This is the quotient chi(g) of the Lie algebra freely generated by two isomorphic copies g and g(psi) of a fixed Lie algebra by the ideal generated by the brackets {[}x,x(psi)] for all x. We exhibit an abelian ideal of chi(g) whose associated quotient is a subdirect sum in g circle plus g circle plus g and we give conditions for this ideal to be finite dimensional. We show that chi(g) has a sub quotient that is isomorphic to the Schur multiplier of g. We prove that chi(g) is finitely presentable or of homological type FP2 if and only if g has the same property, but chi(f) is not of type FP3 if f is a non-abelian free Lie algebra. (C) 2019 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 16/24778-9 - Homological finiteness properties of Lie algebras |
| Grantee: | Luis Augusto de Mendonça |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 15/22064-6 - Homological finiteness properties |
| Grantee: | Luis Augusto de Mendonça |
| Support Opportunities: | Scholarships in Brazil - Doctorate |