On the Harmonic Oscillator Algebra

REFERENCES

• Biyogmam , G. R. ( 2011 ). On the Leibniz (co)homology of the Lie algebra of the Euclidean group . J. Pure Appl. Algebra 215 : 1889 – 1901 .
   Web of Science ®Google Scholar
• Biyogmam , G. R. ( 2013 ). Leibniz homology of the Galilei algebra . J. Math. Phy. 54 : 073514 . http://dx.doi.org/10.1063/1.4816671
   Web of Science ®Google Scholar
• Biyogmam , G. R. ( 2013 ). Leibniz homology of the affine indefinite orthogonal Lie algebra. arxiv:1301.0659v1 .
   Google Scholar
• Cao , J. , Voth , G. ( 1990 ). Modeling physical systems by effective harmonic oscillators: The optimized quadratic approximation . J. Chem. Phys. 92 : 7531 .
   Web of Science ®Google Scholar
• Casas , J. M. , Ladra , M. ( 2007 ). Computing low dimensional Leibniz homology of some perfect Leibniz algebras . Southeast Asian Bull. Math. 34 ( 4 ): 683 – 690 .
   Google Scholar
• Chevalley , C. , Eilenberg , S. ( 1948 ). Cohomology theory of Lie groups and Lie algebras . Trans. Amer. Math. Soc. 63 ( 1 ): 85 – 124 .
   Google Scholar
• Fock , V. ( 1932 ). Konfigurationsraum und zweite Quantulung, Zeitschrift fúr Physik, 75, 622–647. Cf., Selected works, V. A. Fock: Quantum mechanics and quantum field theory, Chapman and Hall, 2004 .
   Google Scholar
• Frabetti , A. (1998). Leibniz homology of dialgebras of matrices. J. Pure Appl. Algebra 29(2):123–141.
   Web of Science ®Google Scholar
• Gao , Y. ( 1999 ). Leibniz Homology of unitary Lie algebras . J. Pure Appl. Algebra 140 ( 1 ): 33 – 56 .
   Web of Science ®Google Scholar
• Loday , J.-L. ( 1992 ). Cyclic Homology . Berlin , Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Loday , J.-L. , Pirashvili , T. ( 1993 ). Universal enveloping algebras of Leibniz algebras and (co)-homology . Math. Annalen 296 ( 1 ): 139 – 158 .
   Web of Science ®Google Scholar
• Loday , J.-L. ( 1993 ). Une Version non commutative des algebres de Lie: Les algebres de Leibniz . L'Enseignement Math. 39 : 269 – 293 .
   Google Scholar
• Lodder , J. M. ( 2008 ). Lie algebras of Hamiltonian vector fields and symplectic manifold . Journal of Lie Theory 18 ( 4 ): 897 – 914 .
   Web of Science ®Google Scholar
• Lodder , J. ( 2012 ). A structure theorem for Leibniz cohomology . Journal of Algebra 355 ( 1 ): 93 – 110 .
   Web of Science ®Google Scholar
• Pirasvili , T. ( 1994 ). On Leibniz homology . Annales de l'institut Fourrier, Grenoble 44 ( 2 ): 401 – 411 .
   Web of Science ®Google Scholar
• Communicated by K. Misra.
   Google Scholar