.svg){kind=logo}
ON CERTAIN ALGEBRAIC STRUCTURES APPEARING IN TITS CONSTRUCTION (NORMAL TRIALITY ALGEBRAS AND LIE ALGEBRAS)
Keywords:
Lie algebras, Jordan algebras, alternative algebras, triple systemsDOI:
https://doi.org/10.17654/0972087124007Abstract
We study a certain concept of algebraic structures in $\mathfrak{A}_0 \otimes \mathfrak{J}_0$ due to Tits arising in the construction of exceptional simple Lie algebra $E_8$ considering bihomogeneous spaces associated with the Lie algebra. Moreover, we exhibit the bisymmetric spaces associated with exceptional simple Lie algebras $F_4, E_6, E_7, E_8$.
Received: February 27, 2024
Accepted: April 3, 2024
References
B. N. Allison, A class of nonassociative algebras with involution containing a class of Jordan algebra, Math. Ann. 237 (1978), 133-156.
M. Gell-Mann, Symmetry of Baryons and Mesons, Phys. Rev. 125 (1962), 1067-1084.
N. Kamiya, On a generalization of structurable algebras, Algebras, Groups and Geometries 9 (1992), 35-47.
N. Kamiya, A construction of quandles associated with quadratic algebras II, RIMS. Kokyuroku (Kyoto Univ.) 2188 (2021), 34-44.
N. Kamiya, On triality relations of certain eight-dimensional algebras, RIMS. Kokyuroku (Kyoto Univ.) 2229 (2022), 52-63.
N. Kamiya, On triality relations of normal triality algebras and Lie algebras, RIMS. Kokyuroku (Kyoto Univ.) 2265 (2023), 121-131.
N. Kamiya, On certain algebraic structures associated with Lie (super) algebras, Nonassociative algebras and related topics II, Springer, Pro. Math. and Statistics 427 (2023), 65-79.
N. Kamiya, On symmetric composition algebras and Lie algebras, preparation.
I. L. Kantor and N. Kamiya, A Peirce decomposition for generalized Jordan triple systems of second order, Comm. Alg. 31 (2003), 5875-5913.
N. Kamiya, D. Mondoc and S. Okubo, A structure theory of (-1,-1)-Freudenthal-Kantor triple systems, Bull. Aust. Math. Soc. 81 (2010), 132-155.
N. Kamiya and D. Mondoc, On constructions of Lie (super)algebras and Freudenthal-Kantor triple systems defined by bilinear forms, J. A. A. 19(11) (2020). Doi: 10.1142/S0219498820502230.
N. Kamiya and S. Okubo, Triality of structurable and pre-structurable algebras, J. Alg. 416 (2014), 58-83.
N. Kamiya and S. Okubo, Algebras satisfying triality and symmetry, A. G. G. 33 (2016), 1-92. Arxiv. 1503.00614.
N. Kamiya and S. Okubo, A triality group of nonassociative algebras with involution, A. G. G. 35 (2018), 113-168. Arxiv. 1609.05892.
N. Kamiya and S. Okubo, Symmetry of Lie algebras associated with Freudenthal-Kantor triple systems, Proc. Edinb. Math. Soc. 89 (2016), 169-192.
S. Okubo, Introduction to Octonion and Other Nonassociative Algebras in Physics, Cambridge Univ. Press, 1995.
S. Okubo, Symmetric triality relations and structurable algebra, Linear Algebras and its Applications 396 (2005), 189-222.
R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, 1966.
J. Tits, Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionnelles, I, Construction, Indag. Math. 28 (1966), 223-237.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
Contact Puspha Publishing House for more info or permissions.
