On pull back Lie algebra bundles
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, given a Lie algebra bundle ε over a topological space X and a continuous map f : Y → X, we construct a pull back Lie algebra bundle f^*(ξ ) over Y and we show that a pull back Lie algebra bundle of a semisimple Lie algebra bundle is also semisimple. We prove that given a Lie algebra bundle ε over X and homotopic continuous maps f_0, f_1 : Y → X, the induced pull back bundles f^*_0 (ξ ) and f^*_1 (ξ ) are isomorphic if Y is compact Hausdorff. Also, we construct an example to show that this result is not true for weak Lie algebra bundles.
Abstract
In this paper, given a Lie algebra bundle ε over a topological space X and a continuous map f : Y → X, we construct a pull back Lie algebra bundle f^*(ξ ) over Y and we show that a pull back Lie algebra bundle of a semisimple Lie algebra bundle is also semisimple. We prove that given a Lie algebra bundle ε over X and homotopic continuous maps f_0, f_1 : Y → X, the induced pull back bundles f^*_0 (ξ ) and f^*_1 (ξ ) are isomorphic if Y is compact Hausdorff. Also, we construct an example to show that this result is not true for weak Lie algebra bundles.
참고문헌 (10)
- M.F. Atiyah, "K-Theory" (1967), W.A.Benjamin Inc
- A. Douady, "Espaces fibres en algebre de Lie et en groupes", Invent. Math, 1, pp.133~151 (1966)
- W. Greub, "Connections, Curvature and Cohomology, Vol.2" (1973), Academic Press
- A. Hatcher, "Vector Bundles and K−Theory", ~ (2003)
- D. Husemoller, "Fibre Bundles, 2nd ed" (1975), Springer-Verlag
- B. S. Kiranagi, "Lie Algebra Bundles", Bull. Sci. math. 2e Serie, 102, pp.57~62 (1978)
- B. S. Kiranagi, "Semisimple Lie Algebra Bundles", Bull. Math. de la Sci. math. de la R.S. de Roumanie, 27(75), pp.253~257 (1983)
- B. S. Kiranagi, "Lie Algebra Bundles and Lie Rings", Proc. Nat. Acd. Sci. India, 54(A), pp.38~44 (1984)
- B. S. Kiranagi, "Rings, Modules and Algebra bundles, In Trends in Theory of Rings and Modules" (2005), Anamaya Publishers
- N. Steenrod, "The Topology of Fibre Bundles" (1951), Princeton University Press