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ON DERIVATION ALGEBRA BUNDLE OF AN ALGEBRA BUNDLE

K. AJAYKUMAR|B.S. Kiranagi|RANJITHA KUMAR|B. MADHU
장전수학회 (Jangjeon Mathematical Society)|2018.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제21권 제2호|pp. 293-300|DOI 10.17777/pjms.2018.21.2.010

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참고문헌

키워드

Algebra bundleLie algebra bundlecharacteristic ideal bundlederivation algebra bundleradical bundlesemisimple algebra bundlevector bundle
주제분류수학

초록

We prove local triviality of a semisimple algebra bundle and that its corresponding Lie algebra bundle is a direct summand of the centre and a semisimple ideal bundle. Further we prove that the radical bundle of an algebra bundle is a characteristic ideal bundle. Using these results we establish that an algebra bundle is semisimple if and only if its derivation algebra bundle is either semisimple or zero.

Abstract

We prove local triviality of a semisimple algebra bundle and that its corresponding Lie algebra bundle is a direct summand of the centre and a semisimple ideal bundle. Further we prove that the radical bundle of an algebra bundle is a characteristic ideal bundle. Using these results we establish that an algebra bundle is semisimple if and only if its derivation algebra bundle is either semisimple or zero.

참고문헌 (20)

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관련 논문AI추천

ON 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 MODULE BUNDLES OVER ALGEBRA BUNDLESB. S. KIRANAGI, H. M. PRASAD, R. RAJENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2021 · 제24권 제2호ENGEL'S AND LIE'S THEOREMS FOR LIE ALGEBRA BUNDLESB MADHU, B S KIRANAGI, K AJAYKUMAR, R. Rangarajan장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제1호Lie algebra bundles and a generalization of Lie group bundlesB.S. Kiranagi, K. AJAYKUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제4호On pull back Lie algebra bundlesB.S. Kiranagi, RANJITHA KUMAR, R. RAJENDRA장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제4호ALGEBRA BUNDLES WHOSE m-DIMENSIONAL COHOMOLOGY MODULES ARE ZEROB.S. Kiranagi, R. Rajendra장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제3호

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