Groups and noncommutative algebra: interactions and applications
Free symmetric and unitary pairs in division rings with involution.
| Full text | |
| Author(s): |
Goncalves, Jairo Z.
Total Authors: 1
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| Document type: | Journal article |
| Source: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 13-pg., 2022-04-15. |
| Abstract | |
Let D be a division ring with center k, char k = p not equal 2, let * be an involution of D, and let D-dagger be the multiplicative group of D. A pair (u, v) is called free symmetric, if it is formed by symmetric elements, and it generates a free non-cyclic subgroup of D-dagger. If U(L) is the enveloping algebra of the non-abelian nilpotent Lie k-algebra L over the field k of characteristic not equal 2, and * is a k-involution of L extended to the field of fractions D of U(L), we show that D-dagger contains free symmetric pairs. We also discuss the consequences of symmetric elements of a normal subgroup being torsion over the center. (AU) | |
| FAPESP's process: | 15/09162-9 - Non commutative algebra and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |