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نگاشت تکانی و عمل گروه خارج قسمتی روی فضای کاهش یافته - K | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 دی 1401 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2023.67370.2269 | ||
| نویسندگان | ||
اکبر دهقان نژاد  1؛ Mohammad Dara2
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| 1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846 -13114, Iran. | ||
| 2School of Math., Iran University of Science and Technology, Tehran, Iran | ||
| چکیده | ||
| In Hamiltonian systems, symmetries on the phase space are important. The symmetry of the Hamiltonian system is describable by the action of a Lie group on the phase space which leads to conservation laws on the system. The conserved quantities have been used by the founders of classical mechanics to eliminate degrees of freedom in the particular systems under investigation. These procedures are called reduction theory. The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system and is a fundamental tool for the study of symplectic reduction. In this theory, given the Hamiltonian action, the quotient of a level set of the moment map by the freely and properly action of an isotropy subgroup to form a new symplectic manifold. By considering the topological properties of the moment map and generalization of the codomain of these maps we are led to the definition of the $k$-moment maps. These maps originated in the study of invariant $k$-covariant tensor on a $G$-manifold $M$. In this paper; we prove that if $G$ has a closed normal subgroup $N$, and $M_{\nu}$ is reduced space by $k$-moment map $\mu$ in regular value $\nu$, then $M_{\nu}$ with quotient group action $G_{\nu}/N_{\nu}$ has a $k$-moment map. | ||
| کلیدواژه‌ها | ||
| &lrm؛ Symplectic Geometry&lrm؛ Hamiltonian Systems&lrm؛ Moment Maps&lrm؛ , &lrm؛ Reduction&lrm | ||
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آمار تعداد مشاهده مقاله: 16 |
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