Invariant bilinear forms under the rigid motions of a regular polygon
Abstract
In this paper, for a positive integer n, we compute the number of all n degree representations for a dihedral group G of order 2m, m ≥ 3. We evaluate dimensions of the spaces of invariant bilinear forms corresponding to each of the representation over the field of complex numbers ℂ (in fact over a number field consisting of a primitive 4mth root of unity). We also, assure that the same results hold equally good when considered over a field of characteristic ≡ 1 (mod 4m}. We explicitly discuss the existence of a non-degenerate invariant bilinear form.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Finite Group Theory Research
Publication details
- Journal / source
- Proyecciones (Antofagasta)
- Publisher
- Universidad Catolica del Norte - Chile
- Volume
- 44
- Issue
- 6
- Pages
- 1069–1084
- Publication date
- 16 February 2026
- Language
- EN