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Some Constructions of Color Hom-Novikov-Poisson Algebras

Year 2019, Volume: 7 Issue: 1, 78 - 86, 30.04.2019
https://izlik.org/JA28LJ23UH

Abstract

The aim of this paper is to introduce color Hom-Novikov-Poisson algebras which generalize color Hom-
Novikov algebras. Many constructions of color Hom-Novikov-Poisson algebras are given either from
color Novikov-Poisson algebras or from ε- commutative Hom-associative color algebras.

References

  • [1] Ammar,F. and Makhlouf, A., Hom-Lie and Hom-Lie-admissible superalgebras, J. algebra. 32(2010), no. 7, 1513-1528.
  • [2] Attan, S., Some characterisations of color Hom-Poisson algebras, Hacet. J. Math. Stat. 47(2018), no. 6, 1552-1563
  • [3] Bakayoko, I., Hom-Novikov color algebras, Arxiv: 1609.07813v1.
  • [4] Bergen, J. and Grzeszuk, P., Simple Jordan color algebras arising from associative graded algebras, J. algebra. 246(2001), no. 2, 915-950.
  • [5] Gao, X. and Xu, L., Novikov color algebras and Torkten color algebras, Journal of Jilin University. 54(2016) , no. 2, 197-201.
  • [6] Gel’fand, I.M. and Dorfman, I.Ya., Hamiltonian operators and algebraic structures related to them, Funct. Anal, App. 13(1979), 248-262.
  • [7] Hartwig, J. T., Larsson, D. and Silvestrov, S.D., Deformations of Lie algebras using -derivations, J. Algebra. 295(2006), no. 2, 314-361.
  • [8] Larsson, D. and Silvestrov, S.D., Quasi-Hom-Lie algebras, central extensions and 2-cycle-like identities, J. Algebra. 288(2005), no. 2, 321-344.
  • [9] Larsson, D. and Silvestrov, S.D., Quasi-Lie algebras, Noncommutative Geometry and representation Theory in Mathematical physics. cotemp. Math., 391, Amer. Math. Soc., Providence, RI. 2005, 241-248.
  • [10] Makhlouf, A. and Silvestrov, S.D., Hom-algebras structures, J. Gen. Lie theory Appl. 2(2008), no. 2, 51-64.
  • [11] Quingcheng, Z. and Yongzeng, Z., Derivations and extensions of lie color algebra, Acta Mathematica Scienta. 28(2008), no. 4, 933-948.
  • [12] Wang, C., Zhang, Q. andWei, Z., Hom-Leibniz superalgebras and Hom-Leibniz-Poisson superalgebras, Hacet. J. Math. Stat. 44(2015), no.5, 1163-1179.
  • [13] Xu, X., On simple Novikov algebras and their irreducible modules, J. Algebra. 185(1996), no. 3, 905-934. [14] Xu, X., Novikov-Poisson algebras, J. algebra. 190(1997), no. 2, 253-279.
  • [15] Xu, X., Variational calculus of supervariables and related algebraic structures, J. Algebra. 223(2000), no. 2, 396-437.
  • [16] Yau, D., Hom-algebras and homology, J. Lie theory. 19(2009), no. 2, 409-421.
  • [17] Yau, D., Hom-Novikov algebras, J. Phys. A. 44(2011), no. 8 085202.
  • [18] Yau, D., A twisted generalization of Novikov-poisson algebras, Arxiv: 1010.3410v1.
  • [19] Yu, H., Zhang,W., Jia, Z. and Zhang, Q., Hom-Novikov-Poisson superalgebras, Journal of Jilin University (Science Edition). 53(2015), no. 4, 606-610.
  • [20] Yuan, L., Hom-Lie color algebra structures, Comm. Alg. 40(2012), no. 2, 575-592.
  • [21] Yuan, L. M., Chen, S. and He, C.X., Hom-Gel’fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras, Acta mathematica Sinica. 33(2017), no. 1, 96-116.
  • [22] Zhang, R., Hou, D. and Bai, C., A Hom-version of the affinizations of balinskii-novikov and Novikov superalgebras, J. math. Phys. 52(2011), no. 2, 023505, 19 pp.

Year 2019, Volume: 7 Issue: 1, 78 - 86, 30.04.2019
https://izlik.org/JA28LJ23UH

Abstract

References

  • [1] Ammar,F. and Makhlouf, A., Hom-Lie and Hom-Lie-admissible superalgebras, J. algebra. 32(2010), no. 7, 1513-1528.
  • [2] Attan, S., Some characterisations of color Hom-Poisson algebras, Hacet. J. Math. Stat. 47(2018), no. 6, 1552-1563
  • [3] Bakayoko, I., Hom-Novikov color algebras, Arxiv: 1609.07813v1.
  • [4] Bergen, J. and Grzeszuk, P., Simple Jordan color algebras arising from associative graded algebras, J. algebra. 246(2001), no. 2, 915-950.
  • [5] Gao, X. and Xu, L., Novikov color algebras and Torkten color algebras, Journal of Jilin University. 54(2016) , no. 2, 197-201.
  • [6] Gel’fand, I.M. and Dorfman, I.Ya., Hamiltonian operators and algebraic structures related to them, Funct. Anal, App. 13(1979), 248-262.
  • [7] Hartwig, J. T., Larsson, D. and Silvestrov, S.D., Deformations of Lie algebras using -derivations, J. Algebra. 295(2006), no. 2, 314-361.
  • [8] Larsson, D. and Silvestrov, S.D., Quasi-Hom-Lie algebras, central extensions and 2-cycle-like identities, J. Algebra. 288(2005), no. 2, 321-344.
  • [9] Larsson, D. and Silvestrov, S.D., Quasi-Lie algebras, Noncommutative Geometry and representation Theory in Mathematical physics. cotemp. Math., 391, Amer. Math. Soc., Providence, RI. 2005, 241-248.
  • [10] Makhlouf, A. and Silvestrov, S.D., Hom-algebras structures, J. Gen. Lie theory Appl. 2(2008), no. 2, 51-64.
  • [11] Quingcheng, Z. and Yongzeng, Z., Derivations and extensions of lie color algebra, Acta Mathematica Scienta. 28(2008), no. 4, 933-948.
  • [12] Wang, C., Zhang, Q. andWei, Z., Hom-Leibniz superalgebras and Hom-Leibniz-Poisson superalgebras, Hacet. J. Math. Stat. 44(2015), no.5, 1163-1179.
  • [13] Xu, X., On simple Novikov algebras and their irreducible modules, J. Algebra. 185(1996), no. 3, 905-934. [14] Xu, X., Novikov-Poisson algebras, J. algebra. 190(1997), no. 2, 253-279.
  • [15] Xu, X., Variational calculus of supervariables and related algebraic structures, J. Algebra. 223(2000), no. 2, 396-437.
  • [16] Yau, D., Hom-algebras and homology, J. Lie theory. 19(2009), no. 2, 409-421.
  • [17] Yau, D., Hom-Novikov algebras, J. Phys. A. 44(2011), no. 8 085202.
  • [18] Yau, D., A twisted generalization of Novikov-poisson algebras, Arxiv: 1010.3410v1.
  • [19] Yu, H., Zhang,W., Jia, Z. and Zhang, Q., Hom-Novikov-Poisson superalgebras, Journal of Jilin University (Science Edition). 53(2015), no. 4, 606-610.
  • [20] Yuan, L., Hom-Lie color algebra structures, Comm. Alg. 40(2012), no. 2, 575-592.
  • [21] Yuan, L. M., Chen, S. and He, C.X., Hom-Gel’fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras, Acta mathematica Sinica. 33(2017), no. 1, 96-116.
  • [22] Zhang, R., Hou, D. and Bai, C., A Hom-version of the affinizations of balinskii-novikov and Novikov superalgebras, J. math. Phys. 52(2011), no. 2, 023505, 19 pp.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Sylvain Attan This is me

Submission Date June 23, 2018
Publication Date April 30, 2019
IZ https://izlik.org/JA28LJ23UH
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Attan, S. (2019). Some Constructions of Color Hom-Novikov-Poisson Algebras. Mathematical Sciences and Applications E-Notes, 7(1), 78-86. https://izlik.org/JA28LJ23UH
AMA 1.Attan S. Some Constructions of Color Hom-Novikov-Poisson Algebras. Math. Sci. Appl. E-Notes. 2019;7(1):78-86. https://izlik.org/JA28LJ23UH
Chicago Attan, Sylvain. 2019. “Some Constructions of Color Hom-Novikov-Poisson Algebras”. Mathematical Sciences and Applications E-Notes 7 (1): 78-86. https://izlik.org/JA28LJ23UH.
EndNote Attan S (April 1, 2019) Some Constructions of Color Hom-Novikov-Poisson Algebras. Mathematical Sciences and Applications E-Notes 7 1 78–86.
IEEE [1]S. Attan, “Some Constructions of Color Hom-Novikov-Poisson Algebras”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 78–86, Apr. 2019, [Online]. Available: https://izlik.org/JA28LJ23UH
ISNAD Attan, Sylvain. “Some Constructions of Color Hom-Novikov-Poisson Algebras”. Mathematical Sciences and Applications E-Notes 7/1 (April 1, 2019): 78-86. https://izlik.org/JA28LJ23UH.
JAMA 1.Attan S. Some Constructions of Color Hom-Novikov-Poisson Algebras. Math. Sci. Appl. E-Notes. 2019;7:78–86.
MLA Attan, Sylvain. “Some Constructions of Color Hom-Novikov-Poisson Algebras”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, Apr. 2019, pp. 78-86, https://izlik.org/JA28LJ23UH.
Vancouver 1.Attan S. Some Constructions of Color Hom-Novikov-Poisson Algebras. Math. Sci. Appl. E-Notes [Internet]. 2019 Apr. 1;7(1):78-86. Available from: https://izlik.org/JA28LJ23UH

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