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Year 2018, Volume: 47 Issue: 6, 1552 - 1563, 12.12.2018

Abstract

References

  • Abdaoui, K., Ammar, F., Makhlouf, A. Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras, Bull. Malays. Math. Sci. Soc., 40 (1), 439-472, 2017.
  • Aizawa, N., Sato, H. q-deformation of the Virasoro algebra with central extension; Phys. Lett. B, 256 (1), 185-190, 1991.
  • Ammar, F., Makhlouf, A. Hom-Lie and Hom-Lie admissible superalgebras, J. Algebra, 324 (7), 1513-1528, 2010.
  • Arnold, V. I. Mathematical methods of classical mechanics, Grad. Texts in Math. 60, Springer, Berlin, 1978.
  • Bakayoko, I. Modules over color Hom-Poisson algebras, J. Gen. Lie Theory Appl., 8 (1) (2014), doi:10.4172/1736-4337.1000212.
  • Chaichian, M., Kulish, P., Lukierski, J. q-Deformed Jacobi identity, q-oscillators and q-deformed infinite-dimensional algebras, Phys. Lett. B., 237 (3)(4), 401-406, 1990.
  • Chari, V., Pressley, A. N. A guide to quantum groups, Cambridge Univ. Press, Cambridge, 1994.
  • Curtright, T. L., Zachos, C. K. Deforming maps for quantum algebras, Phys. Lett. B 243 (3), 237-244, 1990.
  • Drinfel'd, V. G. Quantum groups, in: Proc. ICM (Berkeley, 1986), p.798-820, AMS, Providence, RI, 1987.
  • Frenkel, E., Ben-Zvi, D. Vertex algebras and algebraic curves, Math Surveys and Monographs 88, 2nd ed., AMS, Providence, RI, 2004.
  • Gerstenhaber, M. On the deformation of rings and algebras, Ann. Math., 79, 59-103, 1964.
  • Goze, M., Remm, E. Poisson algebras in terms of non-associative algebras, J. Algebra, 320 (1), 294-317, 2008.
  • Hartwig, J. T., Larsson, D. and Silvestrov, S. D. Deformations of Lie algebras using $\sigma-$derivations, J. Algebra, 295 (2), 314-361, 2006.
  • Hu, N. q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq., 6 (1), 51-70, 1999.
  • Kassel, C. Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Commun. Math. Phys., 146, 343-351, 1992.
  • Kontsevich, M. Deformation quantization of Poisson manifolds, Lett. Math. Phys., 66, 157-216, 2003.
  • Makhlouf, A., Silvestrov, S. D. Hom-algebra structures, J. Gen. Lie Theory Appl., 2 (2) , 51-64, 2008.
  • Makhlouf, A., Silvesrov, S. D. Notes on Formal deformations of Hom-Associative and Hom-Lie algebras, Forum Math., 22 (4), 715-759, 2010.
  • M. Markl, M., E. Remm, E. Algebras with one operation including Poisson and other Lie-admissible algebras, J. Algebra, 299 (1), 171-189, 2006.
  • J. Nan, J., Wang, C. and Zhang, Q. Hom-Malcev superalgebras, Front. Math. China DOI 10.1007/s11464-014-0351-0.
  • Schaller, P., Strobl, T. Poisson structure induced (topological) field theories, Mod. Phys. Lett. A 9, 3129-3136, 1994.
  • Silvestrov, S. D. On the classification of 3-dimensional coloured Lie algebras, Quantum groups and Quantum spaces, Banach Center and publications, 40, 1997.
  • Vaisman, I. Lectures on the geometry of Poisson manifolds, Birkh\"auser, Basel, 1994.
  • Wang, C., Zhang, Q., Wei, Z. Hom-Leibniz superalgebras and Hom-Leibniz poisson superalgebras, Hacet. J. Math. Stat., 44 (5), 1163-1179, 2015.
  • Yau, D. Hom-Malcev, Hom-alternative, and Hom-Jordan algebras, Int. Elect. J. Algebra, 11, 177-217, 2012.
  • Yau, D. Non-commutative Hom-Poisson algebras, e-Print arXiv:1010.3408 (2010).
  • Yuan, L. Hom-Lie color algebras, Comm. Algebra, 40 (2), 575-592, 2012.
  • Yuan, L. M., Chen, S., He, C. X. Hom-Gel'fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras, Acta Math. Sinica, 33 (1), 96-116, 2017.

Some characterizations of color Hom-Poisson algebras

Year 2018, Volume: 47 Issue: 6, 1552 - 1563, 12.12.2018

Abstract

In this paper, we describe color Hom-Poisson structures in terms of a single bilinear operation. This enables us to explore color Hom-Poisson algebras in the realm of non-Hom-associative color algebras.

References

  • Abdaoui, K., Ammar, F., Makhlouf, A. Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras, Bull. Malays. Math. Sci. Soc., 40 (1), 439-472, 2017.
  • Aizawa, N., Sato, H. q-deformation of the Virasoro algebra with central extension; Phys. Lett. B, 256 (1), 185-190, 1991.
  • Ammar, F., Makhlouf, A. Hom-Lie and Hom-Lie admissible superalgebras, J. Algebra, 324 (7), 1513-1528, 2010.
  • Arnold, V. I. Mathematical methods of classical mechanics, Grad. Texts in Math. 60, Springer, Berlin, 1978.
  • Bakayoko, I. Modules over color Hom-Poisson algebras, J. Gen. Lie Theory Appl., 8 (1) (2014), doi:10.4172/1736-4337.1000212.
  • Chaichian, M., Kulish, P., Lukierski, J. q-Deformed Jacobi identity, q-oscillators and q-deformed infinite-dimensional algebras, Phys. Lett. B., 237 (3)(4), 401-406, 1990.
  • Chari, V., Pressley, A. N. A guide to quantum groups, Cambridge Univ. Press, Cambridge, 1994.
  • Curtright, T. L., Zachos, C. K. Deforming maps for quantum algebras, Phys. Lett. B 243 (3), 237-244, 1990.
  • Drinfel'd, V. G. Quantum groups, in: Proc. ICM (Berkeley, 1986), p.798-820, AMS, Providence, RI, 1987.
  • Frenkel, E., Ben-Zvi, D. Vertex algebras and algebraic curves, Math Surveys and Monographs 88, 2nd ed., AMS, Providence, RI, 2004.
  • Gerstenhaber, M. On the deformation of rings and algebras, Ann. Math., 79, 59-103, 1964.
  • Goze, M., Remm, E. Poisson algebras in terms of non-associative algebras, J. Algebra, 320 (1), 294-317, 2008.
  • Hartwig, J. T., Larsson, D. and Silvestrov, S. D. Deformations of Lie algebras using $\sigma-$derivations, J. Algebra, 295 (2), 314-361, 2006.
  • Hu, N. q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq., 6 (1), 51-70, 1999.
  • Kassel, C. Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Commun. Math. Phys., 146, 343-351, 1992.
  • Kontsevich, M. Deformation quantization of Poisson manifolds, Lett. Math. Phys., 66, 157-216, 2003.
  • Makhlouf, A., Silvestrov, S. D. Hom-algebra structures, J. Gen. Lie Theory Appl., 2 (2) , 51-64, 2008.
  • Makhlouf, A., Silvesrov, S. D. Notes on Formal deformations of Hom-Associative and Hom-Lie algebras, Forum Math., 22 (4), 715-759, 2010.
  • M. Markl, M., E. Remm, E. Algebras with one operation including Poisson and other Lie-admissible algebras, J. Algebra, 299 (1), 171-189, 2006.
  • J. Nan, J., Wang, C. and Zhang, Q. Hom-Malcev superalgebras, Front. Math. China DOI 10.1007/s11464-014-0351-0.
  • Schaller, P., Strobl, T. Poisson structure induced (topological) field theories, Mod. Phys. Lett. A 9, 3129-3136, 1994.
  • Silvestrov, S. D. On the classification of 3-dimensional coloured Lie algebras, Quantum groups and Quantum spaces, Banach Center and publications, 40, 1997.
  • Vaisman, I. Lectures on the geometry of Poisson manifolds, Birkh\"auser, Basel, 1994.
  • Wang, C., Zhang, Q., Wei, Z. Hom-Leibniz superalgebras and Hom-Leibniz poisson superalgebras, Hacet. J. Math. Stat., 44 (5), 1163-1179, 2015.
  • Yau, D. Hom-Malcev, Hom-alternative, and Hom-Jordan algebras, Int. Elect. J. Algebra, 11, 177-217, 2012.
  • Yau, D. Non-commutative Hom-Poisson algebras, e-Print arXiv:1010.3408 (2010).
  • Yuan, L. Hom-Lie color algebras, Comm. Algebra, 40 (2), 575-592, 2012.
  • Yuan, L. M., Chen, S., He, C. X. Hom-Gel'fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras, Acta Math. Sinica, 33 (1), 96-116, 2017.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sylvain Attan

Publication Date December 12, 2018
Published in Issue Year 2018 Volume: 47 Issue: 6

Cite

APA Attan, S. (2018). Some characterizations of color Hom-Poisson algebras. Hacettepe Journal of Mathematics and Statistics, 47(6), 1552-1563.
AMA Attan S. Some characterizations of color Hom-Poisson algebras. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1552-1563.
Chicago Attan, Sylvain. “Some Characterizations of Color Hom-Poisson Algebras”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1552-63.
EndNote Attan S (December 1, 2018) Some characterizations of color Hom-Poisson algebras. Hacettepe Journal of Mathematics and Statistics 47 6 1552–1563.
IEEE S. Attan, “Some characterizations of color Hom-Poisson algebras”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1552–1563, 2018.
ISNAD Attan, Sylvain. “Some Characterizations of Color Hom-Poisson Algebras”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 2018), 1552-1563.
JAMA Attan S. Some characterizations of color Hom-Poisson algebras. Hacettepe Journal of Mathematics and Statistics. 2018;47:1552–1563.
MLA Attan, Sylvain. “Some Characterizations of Color Hom-Poisson Algebras”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018, pp. 1552-63.
Vancouver Attan S. Some characterizations of color Hom-Poisson algebras. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1552-63.