| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Mem Univ Newfoundland, St John, NF A1C 5S7 - Canada
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05314970 Sao Paulo - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 12, n. 1 FEB 2013. |
| Web of Science Citations: | 1 |
| Abstract | |
Let G be a group with involution {*} and sigma : G -> [+/- 1] a group homomorphism. The map \# that sends alpha = Sigma alpha(g)g in a group ring RG to alpha(\#) = Sigma sigma(g)alpha(g)g{*} is an involution of RG called an oriented group involution. An element alpha epsilon RG is symmetric if alpha(\#) = alpha and skew-symmetric if alpha(\#) = -alpha. The sets of symmetric and skew-symmetric elements have received a lot of attention in the special cases that {*} is the inverse map on G or sigma is identically 1, while the general case has been almost ignored. In this paper, we determine the conditions under which the set of elements that are skew-symmetric relative to a general oriented involution form a subring of RG. This is the sequel to another paper where the analogous problem for the symmetric elements was studied, with a small oversight that is corrected here. (AU) | |
| FAPESP's process: | 09/52665-0 - Groups, rings and algebras: interactions and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 11/50046-1 - Edgar George Goodaire | University of Newfoundland - Canada |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |