Lie algebras and Lie groups over noncommutative rings
| dc.creator | Berenstein, Arkady | |
| dc.creator | Retakh, Vladimir | |
| dc.date | 2007-01-15 | |
| dc.date | 2008-02-19 | |
| dc.date.accessioned | 2026-07-07T09:21:36Z | |
| dc.date.available | 2026-07-07T09:21:36Z | |
| dc.description | The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra $\gg$ sitting inside an associative algebra $A$ and any associative algebra $\FF$ we introduce and study the algebra $(\gg,A)(\FF)$, which is the Lie subalgebra of $\FF \otimes A$ generated by $\FF \otimes \gg$. In many examples $A$ is the universal enveloping algebra of $\gg$. Our description of the algebra $(\gg,A)(\FF)$ has a striking resemblance to the commutator expansions of $\FF$ used by M. Kapranov in his approach to noncommutative geometry. To each algebra $(\gg, A)(\FF)$ we associate a ``noncommutative algebraic'' group which naturally acts on $(\gg,A)(\FF)$ by conjugations and conclude the paper with some examples of such groups. | |
| dc.description | Introduction is improved and some typos corrected. To appear in "Advances" | |
| dc.identifier | https://arxiv.org/abs/math/0701399 | |
| dc.identifier | http://arxiv.org/abs/math/0701399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155079 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | Lie algebras and Lie groups over noncommutative rings | |
| dc.type | text |