Lie algebras and lie groups over noncommutative rings

• Autores: Arkady Berenstein, Vladimir Retakh
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 6, 2008, págs. 1723-1758
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.03.003
• Texto completo no disponible (Saber más ...)
• Resumen

  • The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra sitting inside an associative algebra A and any associative algebra we introduce and study the algebra , which is the Lie subalgebra of generated by . In many examples A is the universal enveloping algebra of . Our description of the algebra has a striking resemblance to the commutator expansions of used by M. Kapranov in his approach to noncommutative geometry. To each algebra we associate a �noncommutative algebraic� group which naturally acts on by conjugations and conclude the paper with some examples of such groups