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Cohomology and deformations of Hom-Lie-Yamaguti color algebras

A. Nourou Issa
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2021.06|한국수학논문집 (Korean Journal of Mathematics)|제29권 제2호|pp. 271-291

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RepresentationDeformationHom-algebraColor algebra
주제분류수학

초록

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The $(2,3)$-cocycles of a given Hom-Lie-Yamaguti color algebra $T$ are shown to be very useful in a study of its deformations. In particular, it is shown that any $(2,3)$-cocycle of $T$ gives rise to a Hom-Lie-Yamaguti color structure on $T \oplus V$, where $V$ is a $T$-module, and that a one-parameter infinitesimal deformation of $T$ is equivalent to that a $(2,3)$-cocycle of $T$ (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

Abstract

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The $(2,3)$-cocycles of a given Hom-Lie-Yamaguti color algebra $T$ are shown to be very useful in a study of its deformations. In particular, it is shown that any $(2,3)$-cocycle of $T$ gives rise to a Hom-Lie-Yamaguti color structure on $T \oplus V$, where $V$ is a $T$-module, and that a one-parameter infinitesimal deformation of $T$ is equivalent to that a $(2,3)$-cocycle of $T$ (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

참고문헌 (31)

  1. K. Abdaoui, "Constructions and cohomology of Hom-Lie color algebras", Comm. Algebra, 43(11), pp.4581~4612 (2015)
  2. F. Ammar, "Quadratic color Hom-Lie algebras", As-sociative and Nonassociative Algebras and Applications, Springer Proceedings in Mathematics and Statistics book series, 311, pp.287~312 (2020)
  3. F. Ammar, "Cohomology and deformations of Hom-algebras", J. Lie Theory, 21(4), pp.813~836 (2011)
  4. F. Ammar, "Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra", Czechoslovak Math. J, 63(3), pp.721~761 (2013)
  5. A. S. Dzhumadil’daev, "Cohomology of colour Leibniz algebras: pre-simplicial approach", Lie Theory and its Applications in Physics III. Proceedings of the Third International Workshop, pp.124~136 (2000), World Scientific
  6. Donatien Gaparayi, "Hom-Lie-Yamaguti superalgebras", 한국수학논문집, 27(1), pp.175~192 (2019), 강원경기수학회
  7. D. Gaparayi, "A twisted generalization of Lie-Yamaguti algebras", Int. J. Algebra, 6(5-8), pp.339~352 (2012)
  8. D. Gaparayi, "Hom-Akivis superalgebras", J. Algebra Comput. Appl, 6(1), pp.36~51 (2017)
  9. S. Guo, "Representations and deformations of Hom-Lie-Yamaguti su-peralgebras", Adv. Math. Phys, pp.12~ (2020)
  10. J. Hartwig, "Deformations of Lie algebras using σ-derivations", J. Algebra, 295(2), pp.314~361 (2006)
  11. A. N. Issa, "Hom-Akivis algebras", Comment. Math. Univ. Carolinae, 52(4), pp.485~500 (2011)
  12. A. N. Issa, "On Lie-Yamaguti color algebras", Mat. Vesnik, 71(3), pp.196~206 (2019)
  13. Z. Jia, "Nilpotent ideals of Lie color triple systems", J. Jilin Univ. (Science Edition), 49(4), pp.674~678 (2011)
  14. M. Kikkawa, "Geometry of homogeneous Lie loops", Hiroshima Math. J, 5, pp.141~179 (1975)
  15. M. K. Kinyon, "Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces", Amer. J. Math, 123, pp.525~550 (2001)
  16. D. Larsson, "Quasi-Hom-Lie algebras, central extensions and 2-cocycle-like identities", J. Algebra, 288, pp.321~344 (2005)
  17. Y. Ma, "One-parameter formal deformations of Hom-Lie-Yamaguti algebras", J. Math. Phys, 56 (2015)
  18. A. Makhlouf, "Hom-algebra structures", J. Gen. Lie Theory Appl, 2, pp.51~64 (2008)
  19. M. F. Ouedraogo, "Sur les superalg`ebres triples de Lie", pp.1999
  20. R. Ree, "Generalized Lie elements", Canadian J. Math, 12, pp.493~502 (1960)
  21. V. Rittenberg, "Generalized superalgebras", Nuclear Phys. B, 139(3), pp.189~202 (1978)
  22. M. Scheunert, "Generalized Lie algebras", J. Math. Phys, 20(4), pp.712~720 (1979)
  23. Y. Sheng, "Representations of Hom-Lie algebras", Algebra Repr. Theory, 15(6), pp.1081~1098 (2012)
  24. S. D. Silvestrov, "On the classification of 3-dimensional coloured Lie algebras", Quantum Groups and Quantum Spaces, Banach Center Publications, Warszawa, 40, pp.159~170 (1997)
  25. K. Yamaguti, "On the Lie triple system and its generalization", J. Sci. Hiroshima Univ. ser. A, 21, pp.155~160 (1957)
  26. K. Yamaguti, "On cohomology groups of general Lie triple systems", Kumamoto J. Sci. ser. A, 8(3), pp.135~146 (1969)
  27. D. Yau, "Hom-algebras and homology", J. Lie Theory, 19, pp.409~421 (2009)
  28. L. Yuan, "Hom-Lie colour algebra structures", Comm. Alg, 40(2), pp.571~592 (2012)
  29. T. Zhang, "Cohomology and deformations of 3-Lie colour algebras", Linear Mult. Alg, 63, pp.651~671 (2015)
  30. T. Zhang, "Deformations and extensions of Lie-Yamaguti algebras", Linear Mult. Alg, 63(11), pp.2212~2231 (2015)
  31. T. Zhang, "Representations and cohomologies of Hom-Lie-Yamaguti algebras with ap-plications", Colloq. Math, 148(1), pp.131~155 (2017)

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