Department
Mathematics and Statistics
Document Type
Article
Publication Date
6-2017
Abstract
Given a finite-dimensional noncommutative semisimple algebra A over C with involution, we show that A always has a basis B for which ( A , B ) is a reality-based algebra. For algebras that have a one-dimensional representation δ , we show that there always exists an RBA-basis for which δ is a positive degree map. We characterize all RBA-bases of the 5-dimensional noncommutative semisimple algebra for which the algebra has a positive degree map, and give examples of RBA-bases of C ⊕ M n ( C ) for which the RBA has a positive degree map, for all n ≥ 2
Recommended Citation
Herman, A., Muzychuk, M., & Xu, B. (2017). The recognition problem for table algebras and reality-based algebras. Journal of Algebra, 479, 173-191. doi:10.1016/j.jalgebra.2017.01.031
Journal Title
Journal of Algebra
