| تعداد نشریات | 32 |
| تعداد شمارهها | 823 |
| تعداد مقالات | 7,964 |
| تعداد مشاهده مقاله | 41,531,823 |
| تعداد دریافت فایل اصل مقاله | 8,499,463 |
Lie-Yamaguti algebra bundle | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 53-73 اصل مقاله (206.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.26889.1638 | ||
| نویسندگان | ||
| S. Goswami1؛ G. Mukherjee* 2 | ||
| 1Department of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India | ||
| 2Academy of Scientific and Innovative Research (AcSIR), Ghaziabad, India | ||
| چکیده | ||
| We introduce the notion of Lie-Yamaguti algebra bundle, and show that such bundles appeared naturally from geometric considerations in the work of M. Kikkawa. This motivates us to introduce this object in the proper mathematical framework. We define cohomology groups of such bundles with coefficients in a representation extending the definition of cohomology groups of Lie-Yamaguti algebras. | ||
| کلیدواژهها | ||
| Vector bundle؛ Lie-Yamaguti algebra؛ Non-associative algebra؛ Cohomology | ||
| مراجع | ||
|
[1] H. Abdelwahab, E. Barreiro, A. J. Calder´on, and A. F. Ouaridi, The classification of nilpotent Lie-Yamaguti algebras, Linear Algebra and its Applications, 654 (2022), 339–378. [2] P. Benito, M. Bremner and S. Madariaga, Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras, Linear and Multilinear Algebra, 63 (2015), 1257–1281. [3] I. Burdujan, An example of a Lie algebra bundle, Stud. Cerc. Bac˘au, Seria Matem., 10 (2000), 79–88. [4] L. Cantor and D. E. Persists, Differential Geometrical Methods in Mathematical Physics, Lectures Notes in Mathematics, Springer, New York, 1975. [5] ´E. Cartan and J. A. Schouten, On the geometry of the group manifold of simple and semisimple groups, Proc. Acad. Amsterdam, 29 (1926), 803–815. [6] A. Douady and M. Lazard, Espace fibr´es algebr`es de Lie et en groupes, Invent. Math., 1 (1966), 133–151. [7] R. J. Duffin, On the characteristic matrices of covariant systems, Physical Review, 54 (1938), 1114. [8] N. Jacobson, Lie and Jordan triple systems, Amer. J. Math. Soc., 71 (1949), 149–170. [9] P. Jordan, J.V. Neumann and E. Wigner, On an algebraic generalization of the quantum mechanical formation, Annals of Mathematics, 35 (1934), 29–64. [10] N. Kemmer, Particle aspect of meson theory, Proceedings of the Royal Society, 173 (1939), 91–116. [11] N. Kemmer, The algebra of meson matrices, Proceedings of the Cambridge Philosophical Society, 39 (1943), 189–196. [12] M. Kikkawa, On local loops in affine manifolds, J. Sci. Hiroshima Univ. A-I, 28 (1964), 199–207. [13] M. Kikkawa, Geometry of homogeneous Lie loops, Hiroshima Math. J., 5 (1975), 141–179. [14] M. Kikkawa, Geometry of homogeneous left Lie loops and tangent Lie triple algebras, Mem. Fac. Sci. Eng. Shimane Univ. Series B: Mathematical Science, 32 (1999), 57–68. [15] M. K. Kinyon and A. Weinstein, Leibniz algebras, courant algebroids, and multiplications on reductive homogeneous spaces, American J. Math., 123 (2001), 525–550. [16] B. S. Kiranagi, Lie algebra bundles, Bull. Sci. Math., (2) 102 (1978), 57–62. [17] B. S. Kiranagi, B. Madhu and K. Ajaykumar, On Smooth Lie algebra bundles, International Journal of Algebra, (5) 11 (2017), 247–254. [18] B. S. Kiranagi, G. Prema and C. Chidarnbara, Rigidity theorem for Lie algebra bundles, Communications in Algebra, (6) 20 (1992), 1549–1556. [19] R. Kumar, On characteristic ideal bundles of a Lie algebra bundle, Journal of Algebra and Related Topics, (2) 9 (2021), 23–28. [20] R. Kumar, Jordan algebra nundles and Jordan rings, Journal of Algebra and Related Topics, (1) 10 (2022), 113–118. [21] R. Kumar, On derivation of algebra bundle, Journal of Algebra and Related Topics, (1) 11 (2023), 43–48. [22] J. L. Loday, Une version non commutative des alg`ebres de Lie: les alg`ebres de Leibniz, Enseign. Math., 39 (1993), 269–293. [23] K. C. H. Mackenzie, General theory of Lie groupoids and Lie algebroids, London Mathematical Society Lecture Note Series, Cambridge, 2005. [24] K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math, 76 (1954), 33–65. [25] H. M. Prasad, R. Rajendra and B. S. Kiranagi, On exact sequences of module bundles over algebra bundles, Palestine Journal of Mathematics, (1) 12 (2023), 42–49. [26] N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, 1951. [27] K. Yamaguti, On the Lie triple system and its generalization, J. Sci. Hiroshima Univ., 21 (1958), 155–160. [28] K. Yamaguti, On cohomology groups of general Lie triples systems, Kumamoto J. Sci., 84 (1969), 135–146. | ||
|
آمار تعداد مشاهده مقاله: 2 تعداد دریافت فایل اصل مقاله: 1 |
||