논문KCI 등재
ON MODULE BUNDLES OVER ALGEBRA BUNDLES
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초록
We prove some results of module bundles over associative algebra bundles leading to the decomposition theorem for a semisimple module bundle. Using this theorem we show that all module bundles of an algebra bundle ξ are semisimple if and only if the cohomology modules of ξ of dimension greater than or equal to one are zero.
Abstract
We prove some results of module bundles over associative algebra bundles leading to the decomposition theorem for a semisimple module bundle. Using this theorem we show that all module bundles of an algebra bundle ξ are semisimple if and only if the cohomology modules of ξ of dimension greater than or equal to one are zero.
참고문헌 (14)
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- Dale Husemoller, "Fibre bundles" (1966), Springer-Verlag
- Yu. A. Drozd, "Finite dimensional algebras" (1994), Springer-Verlag
- W.Greub, "Connections, curvature, and cohomology, Vol. II" (1973), Academic Press
- B.S. Kiranagi, "Revisiting Hochschild cohomology for algebra bundles", Journal of Algebra and Applications, 7(6), pp.1~31 (2008)
- John W. Milnor, "Characteristic classes" (1974)
- B.S.Kiranagi, "Semisimple Lie alegebra bundles", Bull. Math de la sci. Math. de la R.S. de Roumaine, 27(75) (1983)
- R.W. Richardson, "A rigidity theorem for subalgebras of Lie and associative algebras", Illinois J. Math, 11 (1967)
- G. Prema, "On complete reducibility of module bundles", Bull.Asutal. Math.Soc, 28, pp.401~409 (1983)
- Richard D. Schafer, "Introduction to nonassociative algebras" (1966), Academy Press
- V. S. Varadarajan, "Lie groups, Lie algebras and their representations" (1974), Prentice-Hall
관련 논문AI추천
ALGEBRA BUNDLES WHOSE m-DIMENSIONAL COHOMOLOGY MODULES ARE ZEROB.S. Kiranagi, R. Rajendra장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제3호ON DERIVATION ALGEBRA BUNDLE OF AN ALGEBRA BUNDLEB. MADHU, B.S. Kiranagi, K. AJAYKUMAR, RANJITHA KUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호ON THE RADICAL BUNDLE OF A LIE ALGEBRA BUNDLEB.S. Kiranagi, G.PREMA, RANJITHA KUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제4호On pull back Lie algebra bundlesB.S. Kiranagi, RANJITHA KUMAR, R. RAJENDRA장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제4호Lie algebra bundles and a generalization of Lie group bundlesB.S. Kiranagi, K. AJAYKUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제4호ENGEL'S AND LIE'S THEOREMS FOR LIE ALGEBRA BUNDLESB MADHU, B S KIRANAGI, K AJAYKUMAR, R. Rangarajan장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제1호
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