الملخص
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.
الكلمات المفتاحية
بيانات النشر
- المعرّف الرقمي
- 10.53539/squjs.vol25iss2pp107-111
- المجلة
- مجلة جامعة السلطان قابوس للعلوم, 25(2), 107-111
- الناشر
- جامعة السلطان قابوس
- وصول مفتوح
- وصول مفتوح ذهبي
- الترخيص
- CC BY 4.0
اقتبس هذه المقالة
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.
شيكاغو (المؤلف–التاريخ)
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.
هارفارد
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.
فانكوفر
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.