| Full text | |
| Author(s): |
Total Authors: 2
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| 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
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| 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 Opportunities: | Scholarships in Brazil - Post-Doctoral |