Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (4): 1-7.

• Article •     Next Articles

Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras

HUA Xiu-ying1,  LIU Wen-de2   

  1. 1. School of Applied Sciences, Harbin University of Science and Technology, Harbin  150080, China;
    2. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
  • Received:2013-07-01 Revised:2013-10-01 Online:2014-07-25 Published:2014-07-25

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Abstract: For the problem of the derivations of the even part into
the odd part of the finite-dimensional odd Hamiltonian superalgebras
over a field of characteristic $p>3,$ by using the generating set of
the even part and calculating the action of derivations on its
generating set, the nonnegative $\mathbb{Z}$-homogeneous derivations
of the even part into the odd part were determined. Furthermore, by
applying the properties of the even part, the negative
$\mathbb{Z}$-homogeneous derivations of the even part into the odd
part were given. Therefore, all derivations of the even part into
the odd part of the finite-dimensional odd Hamiltonian superalgebras
were characterized, which has important significance to further
study the structure, the representation and the classification of
Lie superalgebras.

Key words: divided power algebra, derivation, odd Hamiltonian superalgebra

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