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Pullback of lie algebra and lie group bundles, and their homotopy invariance | ||
| Journal of Algebra and Related Topics | ||
| دوره 8، شماره 1، شهریور 2020، صفحه 15-26 اصل مقاله (326.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2020.13988.1156 | ||
| نویسندگان | ||
| K Ajaykumar* 1؛ B. S. Kiranagi2؛ R Rangarajan3 | ||
| 1School of PPSH, Chinmaya Vishwavidyapeeth, Adi Sankara Nilayam, Ernakulam, Kerala, India | ||
| 2Department of Mathematics, University of Mysore,Mysuru | ||
| 3Department of Mathematics, University of Mysore, Mysuru | ||
| چکیده | ||
| We study the pullback Lie algebra (group) bundle of a Lie algebra (group) bundle and show that the Lie algebra bundle of the pullback of a Lie group bundle $\mathfrak{G}$ is isomorphic to the pullback of the Lie algebra bundle of $\mathfrak{G}$. Then, using the notion of Lie connection on a Lie algebra bundle, we show that the pullbacks of a Lie algebra bundle $\xi$ over a smooth manifold $M$ with respect to two smooth homotopic functions $f_0 , f_1 : N \rightarrow M$ are isomorphic to Lie algebra bundles over $N$. | ||
| کلیدواژه‌ها | ||
| Lie algebra and Lie group bundles؛ pullback of bundles؛ principal bundles؛ homotopy invariance | ||
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آمار تعداد مشاهده مقاله: 790 تعداد دریافت فایل اصل مقاله: 1,054 |
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