Dynamics over Cocycyle Double Cross Products
22nd Workshop on Quantization, Dualities and Integrable Systems, İstanbul, Türkiye, 22 - 25 Nisan 2025, ss.18-19, (Özet Bildiri)
- Yayın Türü: Bildiri / Özet Bildiri
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Sayfa Sayıları: ss.18-19
- Maltepe Üniversitesi Adresli: Evet
Özet
Abstract: We present the Euler-Lagrange and Hamilton’s equations for a system whose configuration space is a unified product Lie group G = M ×_γ H, for some γ : M × M → H. By reduction, then, we obtain the Euler-Lagrange type and Hamilton’s type equations of the same form for the quotient space M = G/H, although it is not necessarily a Lie group. We observe, through further reduction, that it is possible to formulate the Euler-Poincaré type and Lie-Poisson type equations on the corresponding quotient m = g/h of Lie algebras, which is not a priori a Lie algebra. We illustrate our results in the realm of the Kepler problem, and the non-linear tokamak plasma dynamics.