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The inversion height of the free field is infinite

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Autor(es):
Herbera, Dolors [1] ; Sanchez, Javier [2]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain
[2] Univ Sao Paulo, IME, Dept Math, BR-05314970 Sao Paulo, SP - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: SELECTA MATHEMATICA-NEW SERIES; v. 21, n. 3, p. 883-929, JUL 2015.
Citações Web of Science: 3
Resumo

Let be a finite set with at least two elements, and let be any commutative field. We prove that the inversion height of the embedding , where denotes the universal (skew) field of fractions of the free algebra , is infinite. Therefore, if denotes the free group on , the inversion height of the embedding of the group algebra into the Malcev-Neumann series ring is also infinite. This answers in the affirmative a question posed by Neumann (Trans Am Math Soc 66:202-252, 1949). We also give an infinite family of examples of non-isomorphic fields of fractions of with infinite inversion height. We show that the universal field of fractions of a crossed product of a field by the universal enveloping algebra of a free Lie algebra is a field of fractions constructed by Cohn (and later by Lichtman). This extends a result by A. Lichtman. (AU)

Processo FAPESP: 09/50886-0 - Embedding group algebras ánd crossed products ín division rings
Beneficiário:Javier Sanchez Serda
Linha de fomento: Bolsas no Brasil - Pós-Doutorado