Novikov-Jordan algebras

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Dzhumadil'daev, A. S.;
  • Subject: Mathematical Physics | 17c50 | Mathematics - Rings and Algebras | Mathematics - Quantum Algebra
    arxiv: Astrophysics::Galaxy Astrophysics | Astrophysics::Cosmology and Extragalactic Astrophysics | Astrophysics::Earth and Planetary Astrophysics | Astrophysics::Solar and Stellar Astrophysics

Algebras with identity $(a\star b)\star (c\star d) -(a\star d)\star(c\star b)$ $=(a,b,c)\star d-(a,d,c)\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is ... View more
  • References (20)
    20 references, page 1 of 2

    [1] A.A. Balinskii, S.P. Novikov, Poisson bracket of hamiltonian type, Frobenius algebras and Lie algebras, Dokladu AN SSSR, 283(1985), No.5, 1036-1039.

    [2] A. Cayley, On the theory of analytical forms called trees, Phil. Mag., 13(1857), 19-30; Mathematical Papers, Cambridge, 3(1891), 242-246.

    [3] A. S. Dzhumadil'daev, Cohomologies and deformations of right-symmetric algebras, J.Math.Sciences, 93(1999), No. 6, 1836-1876. Preprint available math.RT/9807065.

    [4] A. S. Dzhumadil'daev, Minimal identities for right-symmetric algebras, J.Algebra, 225(2000),201-230.

    [5] I.M. Gelfand, I.Ya. Dorfman, Hamiltonian operators and related algebraic structures, Funct. Anal. Prilozhen. 13(1979), No. 4, 13-30= engl.transl. Funct. Anal. Appl. 13(1979), 248-262.

    [6] M. Gerstenhaber, The cohomology structure of an associative ring, Annals of Math.,78(1963), No.2, 267-288.

    [7] P. Holgate, Jordan algebras arising in population genetics, Proc. Edinburg Math. Soc. (2)15(1966-67), 291-294.

    [8] E. Kleinfeld, F. Kosier, J.M. Osborn, D. Rodabaugh, The structure of associator dependent rings, Trans. Amer. Math. Soc. 110(1964), 473-483.

    [9] F. Kosier, J.M. Osborn, Nonassociative algebras satisfying identities of degree three, Trans. Amer. Math. Soc. 110(1964), 484-492.

    [10] J.L. Koszul, Domaines bornĀ“es homog`enes et orbites de groupes de transformations affines, Bull. Soc. Math. France 89(1961), No. 4, 515-533.

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