Algebraic Lie Algebra Bundles and Derivations of Lie Algebra Bundles

Yıl 2024, , 95 - 107, 09.01.2024

M. V. Monica R Rajendra

https://doi.org/10.24330/ieja.1377714

Öz

In this paper, we define algebraic Lie algebra bundles, discuss some results on algebraic Lie algebra bundles and derivations of Lie algebra bundles. Some results involving inner derivations and central derivations of Lie algebra bundles are obtained.

Anahtar Kelimeler

Vector bundle, algebra bundle, derivations of Lie algebra bundle, algebraic Lie algebra bundle

Kaynakça

• M. F. Atiyah, K - Theory, W. A. Benjamin, Inc., New York- Amsterdam, 1967.
• C. Chevalley, A new kind of relationship between matrices, Amer. J. Math., 65 (1943), 521-531.
• C. Chevalley, Algebraic Lie algebras, Ann. of Math. (2), 48 (1947), 91-100.
• C. Chevalley, Theorie des Groupes de Lie, Tome II, Groupes Algebriques, No. 1152. Hermann & Cie, Paris, 1951.
• M. Goto, On algebraic Lie algebras, J. Math. Soc. Japan, 1 (1948), 29-45.
• G. Hochschild, Semi-simple algebras and generalized derivations, Amer. J. Math., 64 (1942), 677-694.
• B. S. Kiranagi, R. Kumar, K. Ajaykumar and B. Madhu, On derivation algebra bundle of an algebra bundle, Proc. Jangjeon Math. Soc., 21(2) (2018), 293-300.
• Y. Matsushima, Note on the replicas of matrices, Proc. Japan Acad., 23(5) (1947), 42-49.
• S.Tôgô, On the derivation algebras of Lie algebras, Canadian J. Math., 13 (1961), 201-216.
• S. Tôgô, On splittable linear Lie algebras, J. Sci. Hiroshima Univ. Ser. A, 18 (1955), 289-306.
• S. Tôgô, Derivations of Lie algebras, J. Sci. Hiroshima Univ. Ser. A-I Math., 28 (1964), 133-158.