Groups and noncommutative algebra: interactions and applications
Graded rings associated to valuations and their relations to tame and deeply r...
Valuation theory of group rings and homology of soluble groups
| Full text | |
| Author(s): |
Sanchez, Javier
[1]
Total Authors: 1
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| Affiliation: | [1] Univ Sao Paulo, Dept Math, IME, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES; v. 72, n. 6, p. 1463-1504, DEC 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We apply the filtered and graded methods developed in earlier works to find (noncommutative) free group algebras in division rings. If L is a Lie algebra, we denote by U(L) its universal enveloping algebra. P. M. Cohn constructed a division ring D-L that contains U(L). We denote by D(L) the division subring of D-L generated by U(L). Let k be a ueld of characteristic zero, and let L be a nonabelian Lie k-algebra. If either L is residually nilpotent or U(L) is an Ore domain, we show that D(L) contains (noncommutative) free group algebras. In those same cases, if L is equipped with an involution, we are able to prove that the free group algebra in D(L) can be chosen generated by symmetric elements in most cases. Let G be a nonabelian residually torsion-free nilpotent group, and let k(G) be the division subring of theMalcev-Neumann series ring generated by the group algebra k{[}G]. If G is equipped with an involution, we show that k(G) contains a (noncommutative) free group algebra generated by symmetric elements. (AU) | |
| FAPESP's process: | 15/09162-9 - Non commutative algebra and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |