Abstract
The orbits space of an irreducible representation of a finite group is a variety whose coordinate ring is finitely generated by homogeneous invariant polynomials. Boris Dubrovin showed that the orbits spaces of the reflection groups acquire the structure of polynomial Frobenius manifolds. Dubrovin’s method to construct examples of Frobenius manifolds on orbits spaces was carried for other linear representations of discrete groups which have in common that the coordinate rings of the orbits spaces are polynomial rings. In this article, we show that the orbits space of an irreducible representation of a dicyclic group acquires two structures of Frobenius manifolds. The coordinate ring of this orbits space is not a polynomial ring.
Keywords
Publication details
- DOI
- 10.53539/squjs.vol25iss2pp107-111
- Journal
- Sultan Qaboos University Journal for Science, 25(2), 107-111
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Dinar, Y. I., & Al-Maamari, Z. (2025). Dicyclic Groups and Frobenius Manifolds. Sultan Qaboos University Journal for Science, 25(2), 107-111. https://doi.org/10.53539/squjs.vol25iss2pp107-111
MLA 9
Dinar, Yassir Ibrahim, and Zainab Al-Maamari. "Dicyclic Groups and Frobenius Manifolds." Sultan Qaboos University Journal for Science, vol. 25, no. 2, 2025, pp. 107-111. https://doi.org/10.53539/squjs.vol25iss2pp107-111.
Chicago (author–date)
Dinar, Yassir Ibrahim, and Zainab Al-Maamari. 2025. "Dicyclic Groups and Frobenius Manifolds." Sultan Qaboos University Journal for Science 25 (2): 107-111. https://doi.org/10.53539/squjs.vol25iss2pp107-111.
Harvard
Dinar, Y. I. and Al-Maamari, Z. (2025) 'Dicyclic Groups and Frobenius Manifolds', Sultan Qaboos University Journal for Science, 25(2), pp. 107-111. doi:10.53539/squjs.vol25iss2pp107-111.
Vancouver
Dinar YI, Al-Maamari Z. Dicyclic Groups and Frobenius Manifolds. Sultan Qaboos University Journal for Science. 2025;25(2):107-111. doi:10.53539/squjs.vol25iss2pp107-111
IEEE
Y. I. Dinar, and Z. Al-Maamari, "Dicyclic Groups and Frobenius Manifolds," Sultan Qaboos University Journal for Science, vol. 25, no. 2, pp. 107-111, 2025, doi: 10.53539/squjs.vol25iss2pp107-111.