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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The inversion height of the free field is infinite

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Author(s):
Herbera, Dolors [1] ; Sanchez, Javier [2]
Total Authors: 2
Affiliation:
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain
[2] Univ Sao Paulo, IME, Dept Math, BR-05314970 Sao Paulo, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: SELECTA MATHEMATICA-NEW SERIES; v. 21, n. 3, p. 883-929, JUL 2015.
Web of Science Citations: 3
Abstract

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)

FAPESP's process: 09/50886-0 - Embedding group algebras and crossed products in division rings
Grantee:Javier Sanchez Serda
Support type: Scholarships in Brazil - Post-Doctorate