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Free algebras generated by symmetric elements inside division rings with involution

Ferreira, Vitor O. Y Goncalves, Jairo Z. Y Sánchez, Javier (2014) Free algebras generated by symmetric elements inside division rings with involution. In: Altencoa6-2014, Agosto 11 al 15 de 2014, Universidad de Nariño - Colombia.

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Resumen

This is a joint work with Vitor O. Ferreira and Jairo Z. Gon ̧calves. For any Lie algebra L over a field, its universal enveloping algebra U (L) can be embedded in a division ring D (L) constructed by Cohn [?] (and simplified later by Lichtman [?]). If U (L) is an Ore domain, D (L) coincides with its ring of fractions. Consider now the principal involution of L, L → L, x 7→ − x. It is well known that the principal involution of L can be extended to an involution of U (L). It was proved by Cimpric, that this involution can be extended to D (L) [?]. For a large class of noncommutative Lie algebras L over a field of zero charac-teristic, we show that D (L) contains noncommutative free algebras generated by symmetric elements (with respect to the extension of the pri ncipal involution). This class contains all noncommutative Lie algebras over a field of zero characteristic such that U(L) is an Ore domain.

Tipo de Elemento: Conferencia o Taller artículo (Speech)
Palabras Clave: Infnite dimensional division rings, Division rings with involution, Free associative algebras, Universal enveloping algebra of a Lie algebra.
Asunto: L Educación > LB Theory and practice of education > LB2300 Higher Education
Division: Facultad de Ciencias Exactas y Naturales > Programa de Licenciatura en Matemáticas > Eventos > Álgebra, Teoría de Números, Combinatoria y Aplicaciones Altencoa - 2014
Depósito de Usuario: Depto Matemáticas y Estadística
Fecha Deposito: 04 Sep 2014 20:05
Ultima Modificación: 04 Sep 2014 20:05
URI: http://sired.udenar.edu.co/id/eprint/115

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