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On Derivation Algebra Bundle | ||
Journal of Algebra and Related Topics | ||
دوره 11، شماره 1، شهریور 2023، صفحه 43-48 اصل مقاله (261.56 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22124/jart.2023.22810.1422 | ||
نویسنده | ||
R. Kumar* | ||
Department of Mathematics School of Applied Sciences REVA University, Bangalore- 560064, India | ||
چکیده | ||
We show that the radical bundle of an algebra bundle is a characteristic ideal bundle. Further we prove an algebra bundle is semisimple if and only if its derivation algebra bundle is either semisimple or zero. | ||
کلیدواژهها | ||
Algebra bundle؛ characteristic ideal bundle؛ radical bundle؛ semisimple algebra bundle؛ vector bundle | ||
مراجع | ||
1. M. F. Atiyah, K-Theory, W.A.Benjamin, Inc., New York, Amsterdam, 1967. 2. C. Chidambara, B. S. Kiranagi, On cohomology of associative algebra bundles, J.Ramanujan math.Soc. (1) 9 (1994), 1-12. 3. D.Coppersmith, A Familly of Lie algebras Not Extendible to A Family of Lie Groups, Proc. Amer. Math. Soc., (2) 66 (1977), 365-366. 4. A. Douady, and M. Lazard,, Espace fibres algebres de Lie et en groupes, Invent. Math., 1 (1966), 133-151. 5. W. Greub, S. Halperin and R.Vanstone, Connections, Curvature and Cohmology, Academic Press, New York, London 2, 1973. 6. G. Hochschild, Semi-Simple Algebras and Generalized Derivations, Amer.J. Math., (1) 64 (1942), 677-694. 7. B.S.Kiranagi, Lie algerbra bundles, Bull. Sci. Math., 2e serie, 102 (1978), 57-62. 8. B.S.Kiranagi and G.Prema, A decomposition theorem of Lie algebra bundles, Comm. in Algebra, (6) 18 (1990), 869-877. 9. B.S. Kiranagi,and G.Prema, Rigidity theorem for Lie algebra bundles, Comm.in Algebra, (6) 20 (1992) 1549-1556. 10. B.S. Kiranagi,and R. Rajendra, Revisiting Hochschild Cohomology for Algebra Bundles, J. Algebra Appl., (6) 7 (2008), 685-715. 11. B.S. Kiranagi, G. Prema and R. Kumar, On the Radical Bundle of a Lie Algebra Bundle, Proc.Jangjeon Math. Soc. (4) 15 (2012), 447-453. 12. R. Kumar, On Wedderburn Principal Theorem for Jordan Algebra Bundles, Commun. Algebra, (4) 49 (2021), 1431-1436. 13. R. Kumar, On Characteristic Ideal Bundles of a Lie Algebra Bundle, J. Algebra Relat. Topics, (2) 9 (2021), 23-28. 14. R. Kumar, Jordan Algebra Bundles and Jordan Rings, J. Algebra Relat. Topics, (1) 10 (2022), 113-118. 15. R. S. Pierce, Associative Algebras, Springer-Verlag New York Heidelberg Berlin. 16. W. Landherr, Uber einfache Lie-sche Ringe, Hamb. Abhandlungen, Band 11(1935), 41-64. | ||
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