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Research Articles

Graded systems of quotients and Martindale-like quotients of graded Lie triple systems

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Pages 1932-1943 | Received 04 Mar 2022, Accepted 23 Sep 2022, Published online: 24 Nov 2022

References

  • Anquela, J. A., García, E., Gómez-Lozano, M. (2004). Maximal algebras of Martindale-like quotients of strongly prime linear Jordan algebras. J. Algebra 280(1):367–383. DOI: 10.1016/j.jalgebra.2004.06.002.
  • Anquela, J. A., McCrimmon, K. (2009). Martindale quotients of Jordan algebras. J. Pure Appl. Algebra 213(3): 299–312.
  • Bierwirth, H., Martn González, C., Sánchez Ortega, J., Siles Molina, M. (2015). Martindale algebras of quotients of graded algebras. Commun. Algebra 43(2):829–846. DOI: 10.1080/00927872.2013.849266.
  • Calderón Martín, A. J. (2016). On the structure of graded Lie triple systems. Bull. Korean Math. Soc. 53(1):163–180.
  • Farnsteiner, R. Central extensions and invariant forms of graded Lie algebras. Algebras Groups Geom. 3(4):431–455.
  • Farnsteiner, R. (1988). Derivations and central extensions of finitely generated graded Lie algebras. J. Algebra 118(1):33–45. DOI: 10.1016/0021-8693(88)90046-4.
  • García, E. (2003). Inheritance of primeness by ideals in Lie algebras. Int. J. Math. Game Theory Algebra 13(6): 481–484.
  • García, E., Lozano, M. G. (2004). Jordan systems of Martindale-like quotients. J. Pure Appl. Algebra 194(1–2): 127–145.
  • García, E., Lozano, M. G. (2013). Quotients in graded Lie algebras. Martindale-like quotients for Kantor pairs and Lie triple systems. Algebras Represent. Theory 16(1):229–238.
  • Guo, W., Chen, L. (2016). Algebras of quotients of Jordan-Lie algebras. Commun. Algebra 44(9):3788–3795. DOI: 10.1080/00927872.2015.1087009.
  • Jordan, P. (1933). Über Verallgemeinerungsm oglichkeiten des Formalismus der Quantenmechanik. Nachr. Ges. Wiss. Gottingen 209–214.
  • Jacobson, N. Lie and Jordan triple systems. Amer. J. Math. 71:149–170. DOI: 10.2307/2372102.
  • Lister, W. G. A structure theory of Lie triple systems. Trans. Amer. Math. Soc. 72:217–242. DOI: 10.1090/S0002-9947-1952-0045702-9.
  • Lin, J., Wang, Y., Deng, S. (2009). T*-extension of Lie triple systems. Linear Algebra Appl. 431(11):2071–2083.
  • Meyberg, K. Lectures on algebras and triple systems. The University of Virginia, Charlottesville, Va. Notes on a course of lectures given during the academic year 1971–1972.
  • Martnez, C. (2001). The ring of fractions of a Jordan algebra. J. Algebra 237(2):798–812.
  • Ma, Y., Chen, L., Lin, J. (2014). Systems of quotients of Lie triple systems. Commun. Algebra 42(8):3339–3349. DOI: 10.1080/00927872.2013.783040.
  • Montaner, F. (2010). Algebras of quotients of Jordan algebras. J. Algebra 323(10):2638–2670. DOI: 10.1016/j.jalgebra.2010.02.019.
  • Nijenhuis, A., Richardson, R. W. Jr. (1966). Cohomology and deformations in graded Lie algebras. Bull. Amer. Math. Soc. 72:1–29. DOI: 10.1090/S0002-9904-1966-11401-5.
  • Nahm, W., Rittenberg, V., Scheunert, M. (1976). The classification of graded Lie algebras. Phys. Lett. B 61(4): 383–384.
  • Ross, L. E. (1964) On representations and cohomology of graded Lie algebras. Thesis (Ph.D.)-University of California, Berkeley.
  • Ross, L. E. (1965). Representations of graded Lie algebras. Trans. Amer. Math. Soc. 120:17–23. DOI: 10.1090/S0002-9947-1965-0185043-1.
  • Siles Molina, M. (2004). Algebras of quotients of Lie algebras. J. Pure Appl. Algebra 188(1–3):175–188.
  • Sánchez Ortega, J., Siles Molina, M. (2010). Algebras of quotients of graded Lie algebras. J. Algebra 323(7): 2002–2015.
  • Utumi, Y. (1956). On quotient rings. Osaka Math. J. 8:1–18.
  • Vinberg, È. B. (1975). The classification of nilpotent elements of graded Lie algebras. Dokl. Akad. Nauk SSSR 225(4):745–748 (Russian).
  • Welte, A. (2009). Central extensions of graded Lie algebras. Thesis (Ph.D.)-University of Ottawa (Canada).
  • Yamaguti, K. (1960). On the cohomology space of Lie triple system. Kumamoto J. Sci. Ser. A 5:44–52.
  • Yamaguti, K. (1967/69). On weak representations of Lie triple systems. Kumamoto J. Sci. Ser. A 8:107–114.
  • Yao, C., Ma, Y., Tang, L., Chen, L. (2021). Systems of quotients and Martindale-like quotients of Jordan-Lie triple systems. Commun. Algebra 49(10):4360–4375. DOI: 10.1080/00927872.2021.1920028.

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