47
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Constructions and generalized derivations of multiplicative n-BiHom-Lie color algebras

&
Pages 1982-2014 | Received 18 Sep 2020, Accepted 28 Oct 2023, Published online: 14 Nov 2023

References

  • Abdaoui, K., Ammar, F., Makhlouf, A. (2015). Constructions and cohomology of Hom-Lie color algebras. Commun. Algebra 43(11):4581–4612. DOI: 10.1080/00927872.2014.910797.
  • Abdaoui, K., Hassine, A. B., Makhlouf, A. (2017). BiHom-Lie colour algebras structures, arXiv:1706.02188 [math.RA].
  • Abramov, V., Silvestrov, S. (2020). 3-Hom-Lie algebras based on σ-derivation and involution. Adv. Appl. Clifford Algebras 30:45. DOI: 10.1007/s00006-020-01068-6.
  • Ammar, F., Ayadi, I., Mabrouk, S., Makhlouf, A. (2012). Quadratic color Hom-Lie algebras, arXiv:1204.5155 [math.RA].
  • Ammar, F., Ejbehi, Z., Makhlouf, A. (2011). Cohomology and deformations of Hom-algebras. J. Lie Theory 21(4):813–836.
  • Armakan, A., Silvestrov, S., Farhangdoost, M. R. (2019). Enveloping algebras of color Hom-Lie algebras. Turk. J. Math. 43:316–339. (arXiv:1709.06164 [math.QA] (2017)). DOI: 10.3906/mat-1808-96.
  • Armakan, A., Silvestrov, S., Farhangdoost, M. R. (2021). Extensions of hom-Lie color algebras. Georgian Math. J. 28(1):15–27. (arXiv:1709.08620 [math.QA]). DOI: 10.1515/gmj-2019-2033.
  • Armakan, A., Silvestrov, S. (2023). Color Hom-Lie algebras, color Hom-Leibniz algebras and color omni-Hom-Lie algebras. In: Silvestrov, S., Malyarenko, A., eds. Non-commutative and Nonassociative Algebra and Analysis Structures. SPAS 2019. Springer Proceedings in Mathematics and Statistics, Vol. 426. Cham: Springer. (arXiv:2010.06160v1[math.RA]).
  • Arnlind, J., Kitouni, A., Makhlouf, A., Silvestrov, S. (2014). Structure and cohomology of 3-Lie algebras induced by Lie algebras. In: Makhlouf, A., Paal, E., Silvestrov, S. D., Stolin, A., eds. Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics and Statistics, Vol. 85. Berlin: Springer, pp. 123–144.
  • Arnlind, J., Makhlouf, A., Silvestrov, S. (2010). Ternary Hom-Nambu-Lie algebras induced by HomLie algebras. J. Math. Phys. 51(4):043515.
  • Arnlind, J., Makhlouf, A., Silvestrov, S. (2011). Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras. J. Math. Phys. 52(12):123502.
  • Bagger, J., Lambert, N. (2008). Gauge symmetry and supersymmetry of multiple M2-branes. Phys. Rev. D. 77(6):065008.
  • Bakayoko, I., Manga, B. (2022). Central extensions and Hom-quadratic Hom-Novikov color algebras, nonlinear analysis, geometry and applications. In: Proceedings of the Second NLAGA-BIRS Symposium, Cap Skirring, Senegal. Chap. 22, pp. 25–30.
  • Bakayoko, I., Silvestrov, S. (2020). Multiplicative n-Hom-Lie color algebras. In: Silvestrov, S., Malyarenko, A., Rancić, M., eds. Algebraic Structures and Applications, Springer Proceedings in Mathematics and Statistics, 317. Cham: Springer, pp. 159–187. (arXiv:1912.10216[math.QA])
  • Bakayoko, I., Silvestrov, S. (2021). Hom-left-symmetric color dialgebras, Hom-tridendriform color algebras and Yau’s twisting generalizations. Afr. Mat. 32:941–958. (arXiv:1912.01441 [math.RA]) DOI: 10.1007/s13370-021-00871-z.
  • Benayadi, S., Makhlouf, A. (2014). Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. J. Geom. Phys. 76:38–60. DOI: 10.1016/j.geomphys.2013.10.010.
  • Ben Abdeljelil, A., Elhamdadi, M., Makhlouf, A. (2017). Derivations of ternary Lie algebras and generalizations. Int. Electron. J. Algebra 21:55–75. DOI: 10.24330/ieja.296030.
  • Ben Hassine, A., Chtioui, T., Mabrouk, S., Silvestrov, S. (2021). Structure and cohomology of 3-Lie Rinehart superalgebras. Commun. Algebra 49(11):4883–4904. (arXiv:2010.01237v1 [math.RA]) DOI: 10.1080/00927872.2021.1931266.
  • Bertram, W. (2000). The Geometry of Jordan and Lie Structures. Lectures Notes in Mathematics, Vol. 1754. Berlin: Springer.
  • Chen, C. W., Petit, T., Van Oystaeyen, F. (2006). Note on cohomology of color Hopf and Lie algebras. J. Algebra 299:419–442. DOI: 10.1016/j.jalgebra.2005.11.026.
  • Chen, X.-W., Silvestrov, S. D., van Oystaeyen, F. (2006). Representations and cocycle twists of color Lie algebras. Algebras Represent. Theory 9(6):633–650. DOI: 10.1007/s10468-006-9027-0.
  • Chtioui, T., Mabrouk, S., Makhlouf, A. (2019). BiHom-pre-alternative algebras and BiHom-altenative quadri-algebas, arXiv:1903.03994 [math.RA]
  • Chu, C.-H. (2008). Jordan triples and Riemannian symmetric spaces. Adv. Math. 219:2029–2057. DOI: 10.1016/j.aim.2008.08.001.
  • De Azcarraga, J. A., Izquierdo, J. M. (2011). On a class of n-Leibniz deformations of the simple Filippov algebras. J. Math. Phys. 52(2):023521.
  • Figueroa-O’Farrill, J. (2009). Deformations of 3-algebras. J. Math. Phys. 50(11):113514.
  • Graziani, G., Makhlouf, A., Menini, C., Panaite, F. (2015). BiHom-associative algebras, BiHom-Lie algebras and BiHom-Bialgebras. SIGMA Symmetry Integrability Geom. Methods Appl. 11:086 (34 p.). DOI: 10.3842/SIGMA.2015.086.
  • Günaydin, M., Hyun, S. (1991). Ternary algebraic construction of extended superconformal algebras. Modern Phys. Lett. A. 6:1733–1743. DOI: 10.1142/S0217732391001871.
  • Günaydin, M., Hyun, S. (1992). Ternary algebraic approach to extended superconformal algebras. Nuclear Phys. B. 373:688–712. DOI: 10.1016/0550-3213(92)90271-C.
  • Günaydin, M. (1991). N = 2 superconformal algebras and Jordan triple systems. Phys. Lett. B. 255:46–50. DOI: 10.1016/0370-2693(91)91137-K.
  • Guo, S., Wang, S. (2019). On split regular BiHom-Leibniz superalgebras, arXiv:1903.12474 [math.RA].
  • Guo, S., Zhang, X., Wang, S. (2018). The construction and deformation of BiHom-Novikov algebras. J. Geom. Phys. 132:460–472. DOI: 10.1016/j.geomphys.2018.06.011.
  • Hartwig, J. T., Larsson, D., Silvestrov, S. D. (2006). Deformations of Lie algebras using σ-derivations. J. Algebra 295:314–361. (Preprint in Mathematical Sciences 2003:32, LUTFMA-5036-2003, Centre for Mathematical Sciences, Lund University, 52 pp. (2003)).
  • Jacobson, N. (1949). Lie and Jordan triple systems. Amer. J. Math. 71:149–170. DOI: 10.2307/2372102.
  • Kantor, I. L. (1964). Classification of irreducible transitive differential groups. Dokl. Akad. Nauk SSSR 158:1271–1274.
  • Kaup, W. (1983). die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension II. Math. Ann. 262(7):5–57. DOI: 10.1007/BF01474170.
  • Kaup, W. (1983). A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z. 183:503–529. DOI: 10.1007/BF01173928.
  • Kaygorodov, I. (2011). (n+1)-Ary derivations of simple n-ary algebras. Algebra Logic 50(5):470–471.
  • Kaygorodov, I., Popov, Y. (2016). Generalized derivations of (color) n-ary algebras. Linear Multilinear Algebra 64(6):1086–1106. DOI: 10.1080/03081087.2015.1072492.
  • Kitouni, A., Makhlouf, A., Silvestrov, S. (2020). On n-ary generalization of BiHom-Lie algebras and BiHom-associative algebras. In: Silvestrov, S., Malyarenko, A., Rancic, M., eds. Algebraic Structures and Applications. Springer Proceedings in Mathematics and Statistics, Vol 317. Cham: Springer. (arXiv:1812.00094v1 [math.RA])
  • Koecher, M. (1967). Imbedding of Jordan algebras into Lie algebras, I. Amer. J. Math. 89:787–816. DOI: 10.2307/2373242.
  • Laraiedh, I. (2021). Constructions and T∗-extensions of 3-BiHom-Lie superalgebras. Adv. Appl. Cliff. Algebras 31:20.
  • Laraiedh, I. (2023). Bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras. Hacet. J. Math. Stat. 52(3):673–697.
  • Larsson, D., Silvestrov, S. D. (2005). Quasi-Lie algebras. In: Noncommutative Geometry and Representation Theory in Mathematical Physics. Contemporary Mathematics, 391. Providence, RI: American Mathematical Society, pp. 241–248. (Preprints in Mathematical Sciences 2004:30, LUTFMA-5049-2004, Centre for Mathematical Sciences, Lund University (2004))
  • Larsson, D., Silvestrov, S. D. (2005). Graded quasi-Lie algebras. Czechoslovak J. Phys. 55:1473–1478. DOI: 10.1007/s10582-006-0028-3.
  • Larsson, D., Silvestrov, S. D. (2005). Quasi-Hom-Lie algebras, central extensions and 2-cocycle like identities. J. Algebra 288:321–344. (Preprints in Mathematical Sciences 2004:3, LUTFMA-5038-2004, Centre for Mathematical Sciences, Lund University (2004)) DOI: 10.1016/j.jalgebra.2005.02.032.
  • Leger, G., Luks, E. (2000). Generalized derivations of Lie algebras. J. Algebra 228:165–203. DOI: 10.1006/jabr.1999.8250.
  • Lister, W. G. (1952). A structure theory of Lie triple systems. Trans. Amer. Math. Soc. 72:217–242. DOI: 10.1090/S0002-9947-1952-0045702-9.
  • Liu, L., Makhlouf, A., Menini A. C., Panaite, F. (2020). Rota-Baxter operators on BiHom-associative algebras and related structures. Colloq. Math. 161(2):263–294. DOI: 10.4064/cm7877-5-2019.
  • Li, J., Chen, L. (2020). The construction of 3-Bihom-Lie algebras. Commun. Algebra 48(12):5374–5390. DOI: 10.1080/00927872.2020.1788570.
  • Loos, O. (1969). Symmetric Spaces. I: General Theory. New York-Amsterdam: W. A. Benjamin.
  • Loos, O. (1971). Jordan triple systems, R-spaces, and bounded symmetric domains. Bull. Amer. Math. Soc. 77:558–561. DOI: 10.1090/S0002-9904-1971-12753-2.
  • Mabrouk, S., Ncib, O., Silvestrov, S. (2021). Generalized derivations and Rota-Baxter operators of nary Hom-Nambu superalgebras. Adv. Appl. Clifford Algebras 31:32. (arXiv:2003.01080[math.QA]) DOI: 10.1007/s00006-020-01115-2.
  • Makhlouf, A. (2010). Hom-Alternative algebras and Hom-Jordan algebras. Int. Elect. J. Alg. 8:177–190.
  • Makhlouf, A., Silvestrov, S. (2009). Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras. In: Silvestrov, S., Paal, E., Abramov, V., Stolin, A., eds. Generalized Lie Theory in Mathematics, Physics and Beyond, Berlin, Heidelberg: Springer-Verlag, pp. 189–206.
  • Makhlouf, A., Silvestrov, S. D. (2010). Hom-algebras and Hom-coalgebras. J. Algebra Appl. 9(04):553–589. (Preprints in Mathematical Sciences, Lund University, Centre for Mathematical Sciences, Centrum Scientiarum Mathematicarum, (2008:19) LUTFMA-5103-2008. arXiv:0811.0400 [math.RA] (2008))
  • Makhlouf, A., Silvestrov, S. (2010). Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras. Forum Math. 22(4):715–739. (Preprints in Mathematical Sciences, Lund University, Centre for Mathematical Sciences, Centrum Scientiarum Mathematicarum, (2007:31) LUTFMA-5095-2007. arXiv:0712.3130v1 [math.RA] (2007)).
  • Meyberg, K. (1970). Jordan-Tripelsysteme und die Koecher-Konstruktion von Lie-Algebren. Math. Z. 115:58–78. DOI: 10.1007/BF01109749.
  • Meyberg, K. (1972). Lectures on Algebras and Triple Systems, Lecture Notes. Charlottesville: University of Virginia.
  • Nambu, Y. (1973). Generalized Hamiltonian dynamics. Phys. Rev. D. 8:2405–2412. DOI: 10.1103/PhysRevD.7.2405.
  • Neher, E. (1985). On the classification of Lie and Jordan triple systems. Commun. Algebra 13:2615–2667. DOI: 10.1080/00927878508823293.
  • Piontkovski, D., Silvestrov, S. (2007). Cohomology of 3-dimensional color Lie algebras. J. Algebra 316(2):499–513. DOI: 10.1016/j.jalgebra.2006.11.008.
  • Scheunert, M. (1979). Generalized Lie algebras. J. Math. Phys. 20(4):712–720. DOI: 10.1063/1.524113.
  • Scheunert, M., Zhang, R. (1998). Cohomology of Lie superalgebras and their generalizations. J. Math. Phys. 39:5024–5061. DOI: 10.1063/1.532508.
  • Sheng, Y. (2012). Representation of Hom-Lie algebras. Algebras Represent. Theory 15(6):1081–1098. DOI: 10.1007/s10468-011-9280-8.
  • Sigurdsson, G., Silvestrov, S. D. (2006). Graded quasi-Lie algebras of Witt type. Czech. J. Phys. 56(10–11):1287–1291. DOI: 10.1007/s10582-006-0439-1.
  • Sigurdsson, G., Silvestrov, S. D. (2009). Lie color and Hom-Lie algebras of Witt type and their central extensions. In: Silvestrov, S., Paal, E., Abramov, V., Stolin, A., eds. Generalized Lie Theory in Mathematics, Physics and Beyond. Berlin, Heidelberg: Springer-Verlag, pp. 247–255.
  • Silvestrov, S. D. (1997). On the classification of 3-dimensional coloured Lie algebras. In: Quantum Groups and Quantum Spaces (Warsaw, 1995), Banach Center Publications, 40. Warsaw: Polish Academy of Sciences, pp. 159–170.
  • Tits, J. (1962). Une classe d’algèbres de Lie en relation avec les algèbres de Jordan. Indag. Math. 24:530–535. DOI: 10.1016/S1385-7258(62)50051-6.
  • Yau, D. (2008). Enveloping algebras of Hom-Lie algebras. J. Gen. Lie Theory Appl. 2:95–108. DOI: 10.4303/jglta/S070209.
  • Yau, D. (2009). Hom-algebras and homology. J. Lie Theory 19:409–421.
  • Zhang, T. Deformations and Extensions of 3-Lie Algebras, arXiv:1401.4656 [math.QA]
  • Zhang, R., Zhang, Y. (2010). Generalized derivations of Lie superalgebras. Commun. Algebra 38:3737–3751. DOI: 10.1080/00927870903236228.
  • Zhelyabin, V., Kaygorodov, I. (2012). On d-superderivations of simple superalgebras of Jordan brackets. St. Petersburg Math. J. 23(4):665–677. DOI: 10.1090/S1061-0022-2012-01213-6.
  • Zhou, J., Chen, L., Ma, Y. (2018). Generalized Derivations of Hom-Lie triple systems. Bull. Malaysian Math. Sci. Soc. 41:637–656.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.