cohomology-and-crossed-module-extensions-of-hom-leibniz–rinehart-algebras-|-frontiers-of-mathematics-–-springer

Cohomology and Crossed Module Extensions of Hom-Leibniz–Rinehart Algebras | Frontiers of Mathematics – Springer

References

  1. Albeverio S.A., Ayupov S.A., Omirov B.A., Cartan subalgebras, weight spaces, and criterion of solvability of finite-dimensional Leibniz algebras. Rev. Mat. Complut., 2006, 19(1): 183–195

    MathSciNet  Google Scholar 

  2. Alp M., Pullback crossed modules of algebroids. Iran. J. Sci. Technol. Trans. A Sci., 2008, 32(1): 1–5

    MathSciNet  Google Scholar 

  3. Alp M., Pushout crossed modules of algebroids. Iran. J. Sci. Technol. Trans. A Sci., 2008, 32(3): 175–181

    MathSciNet  Google Scholar 

  4. Alp M., Cat1-Lie–Rinehart algebras. In: Mathematical Applications in Modern Science, Mathematics and Computers in Science and Engineering Series, 38, Athens: WSEAS Press, 2014, 70–73

    Google Scholar 

  5. Barnes D.W., On Levi’s theorem for Leibniz algebras. Bull. Aust. Math. Soc., 2012, 86(2): 184–185

    Article  MathSciNet  Google Scholar 

  6. Blokh A.M., On a generalization of the concept of a Lie algebra. Dokl. Akad. Nauk SSSR, 1965, 165: 471–473

    MathSciNet  Google Scholar 

  7. Casas J.M., Çetin S., Uslu E.Ö., Crossed modules in the category of Loday QD-Rinehart algebras. Homology Homotopy Appl., 2020, 22(2): 347–366

    Article  MathSciNet  Google Scholar 

  8. Casas J.M., Khmaladze E., Pacheco N., A non-abelian tensor product of Hom-Lie algebras. Bull. Malays. Math. Sci. Soc., 2017, 40(3): 1035–1054

    Article  MathSciNet  Google Scholar 

  9. Casas J.M., Ladra M., Omirov B.A., Karimjanov I.A., Classification of solvable Leibniz algebras with null-filiform nilradical. Linear Multilinear Algebra, 2013, 61(6): 758–774

    Article  MathSciNet  Google Scholar 

  10. Casas J.M., Ladra M., Pirashvili T., Crossed modules for Lie–Rinehart algebras. J. Algebra, 2004, 274(1): 192–201

    Article  MathSciNet  Google Scholar 

  11. Cuvier C., Algèbres de Leibnitz: définitions, propriétés. Ann. Sci. Écol. Norm. Sup. (4), 1994, 27(1): 1–45

    Article  MathSciNet  Google Scholar 

  12. Gao Y., Leibniz homology of unitary Lie algebras. J. Pure Appl. Algebra, 1999, 140(1): 33–56

    Article  MathSciNet  Google Scholar 

  13. Gao Y., The second Leibniz homology group for Kac–Moody Lie algebras. Bull. London Math. Soc., 2000, 32(1): 25–33

    Article  MathSciNet  Google Scholar 

  14. Guo S., Zhang X., Wang S., On split regular Hom-Leibniz–Rinehart algebras. J. Math. Res. Appl., 2022, 42(5): 481–498

    MathSciNet  Google Scholar 

  15. Hartwig J., Larsson D., Silvestrov S., Deformations of Lie algebras using σ-derivations. J. Algebra, 2006, 295(2): 314–361

    Article  MathSciNet  Google Scholar 

  16. Herz J.C., Pseudo-algèbres de Lie. I. C. R. Acad. Sci. Paris, 1953, 236: 1935–1937

    Google Scholar 

  17. Huebschmann J., Poisson cohomology and quantization. J. Reine Angew. Math., 1990, 408: 57–113

    MathSciNet  Google Scholar 

  18. Huebschmann J., Duality for Lie–Rinehart algebras and the modular class. J. Reine Angew. Math., 1999, 510: 103–159

    Article  MathSciNet  Google Scholar 

  19. Laurent-Gengoux C., Teles J., Hom-Lie algebroids. J. Geom. Phys., 2013, 68: 69–75

    Article  MathSciNet  Google Scholar 

  20. Liu D., Lin L., On the toroidal Leibniz algebras. Acta Math. Sin. (Engl. Ser.), 2008, 24(2): 227–240

    Article  MathSciNet  Google Scholar 

  21. Loday J.-L., Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign. Math. (2), 1993, 39(3–4): 269–293

    MathSciNet  Google Scholar 

  22. Loday J.-L., Pirashvili T., Universal enveloping algebra of Leibniz algebras and (co)homology. Math. Ann., 1993, 296(1): 139–158

    Article  MathSciNet  Google Scholar 

  23. Mackenzie K., Lie Groupoids and Lie Algebroids in Differential Geometry. London Mathematical Society Lecture Note Series, Cambridge: Cambridge University Press, 1987, 124: xvi+327 pp.

    Book  Google Scholar 

  24. Makhlouf A., Silvestrov S., Hom-algebra structures. J. Gen. Lie Theory Appl., 2008, 2(2): 51–64

    Article  MathSciNet  Google Scholar 

  25. Makhlouf A., Silvestrov S., Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras. Forum Math., 2010, 22(4): 715–739

    Article  MathSciNet  Google Scholar 

  26. Mandal A., Kumar Mishra S., Hom-Lie–Rinehart algebras. Comm. Algebra, 2018, 46(9): 3722–3744

    Article  MathSciNet  Google Scholar 

  27. Omirov B.A., Conjugacy of Cartan subalgebras of complex finite-dimensional Leibniz algebras. J. Algebra, 2006, 302(2): 887–896

    Article  MathSciNet  Google Scholar 

  28. Palais R.S., The cohomology of Lie rings. Proc. Sympos. Pure Math., Providence, RI: Amer. Math. Soc., 1961, 3: 130–137

    Article  MathSciNet  Google Scholar 

  29. Rinehart G.S., Differential forms on general commutative algebras. Trans. Amer. Math. Soc., 1963, 108: 195–222

    Article  MathSciNet  Google Scholar 

  30. Sheng Y., Representations of Hom-Lie algebras. Algebr. Represent. Theory, 2012, 15(6): 1081–1098

    Article  MathSciNet  Google Scholar 

  31. Wang Q., Tan S., Leibniz central extension on a Block Lie algebra. Algebra Colloq., 2007, 14(4): 713–720

    Article  MathSciNet  Google Scholar 

  32. Yau D., Enveloping algebras of Hom-Lie algebras. J. Gen. Lie Theory Appl., 2008, 2(2): 95–108

    Article  MathSciNet  Google Scholar 

  33. Zhang T., Han F.Y., Bi Y.H., Crossed modules for Hom-Lie-Rinehart algebras. Colloq. Math., 2018, 152(1): 1–14

    Article  MathSciNet  Google Scholar 

  34. Zhang T., Zhang H.Y., Crossed modules for Hom-Lie antialgebras. J. Algebra Appl., 2022, 21(7): Paper No. 2250135, 23 pp.

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