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On cohomology for module bundles over associative algebra bundles | ||
| Journal of Algebra and Related Topics | ||
| دوره 12، شماره 1، مهر 2024، صفحه 13-21 اصل مقاله (279.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.23522.1479 | ||
| نویسندگان | ||
| H. M. Prasad1؛ R. Rajendra* 1؛ B. S. Kiranagi2 | ||
| 1Department of Mathematics, Field Marshal K.M. Cariappa College, (A Constituent College of Mangalore University), Madikeri, India | ||
| 2Department of Mathematics, Mangalore University, Mangala- gangothri and Department of Mathematics, University of Mysore, Man-asagangotri , India | ||
| چکیده | ||
| We define cohomology of module bundles over associative algebra bundles. We establish a one to one correspondence between the first cohomology classes and the extensions of module bundles. Using this correspondence we give sufficient condition in terms of cohomology for an algebra bundle to be semisimple. | ||
| کلیدواژه‌ها | ||
| Vector bundle؛ Algebra bundle؛ Module bundle؛ Cohomology | ||
| مراجع | ||
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1. K. Ajaykumar, B. S. Kiranagi and R. Rangarajan, Pullback of Lie algebra and Lie group bundles and their homotopy invariance, J. Algebra Appl. (1) 8 (2020), 15-26. 2. M. F. Atiyah, K-Theory, W.A.Benjamin, Inc., New York, Amsterdam, 1967. 3. C. Chidambara and B. S. Kiranagi, On cohomology of associative algebra bun- dles, J. Ramanujan Math. Soc., (1) 9 (1994), 1-12. 4. W. Greub, S. Halperin and R. Vanston, Connections, curvature, and cohomol- ogy, Vol. II, Academic Press, New York, London, 1973. 5. B. S. Kiranagi and R. Rajendra, Revisiting Hochschild cohomology for algebra bundles, J. Algebra Appl. (6) 7 (2008), 685-715. 6. R. Kumar, On characteristic ideal bundles of a Lie algebra bundle, J. Algebra Appl. (2) 9 (2021), 23-28. 7. R. Kumar, Jordan algebra bundles and Jordan rings, J. Algebra Relat. Topics, (1) 10 (2022), 113-118. 8. G. Prema and B. S. Kiranagi, On complete reducibility of module bundles, Bull.Asutal. Math.Soc., 28 (1983), 401-409. 9. R. D. Schafer, Introduction to nonassociative algebras, Academy Press, New York and London, 1966. 10. D. S. Trustin, Cohomology for modules over associative algebras, J. Algebra, 51 (1978), 550-561. | ||
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آمار تعداد مشاهده مقاله: 109 تعداد دریافت فایل اصل مقاله: 227 |
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