Journal of Lie Theory Vol. 12, No. 2, pp. 583596 (2002) 

A Leibniz algebra structure on the second tensor powerR. Kurdiani and T. PirashviliR. Kurdiani and T. PirashviliA. Razmadze Mathematical Institute Aleksidze str. 1, Tbilisi, 380093, Georgia rezo@rmi.acnet.ge pira@rmi.acnet.ge Abstract: For any Lie algebra $\g$, the bracket $[x\tp y,a\tp b]:=[x,[a,b]]\tp y+x\tp [y,[a,b]]$ defines a Leibniz algebra structure on the vector space $\g \tp \g$. We let $\g\utp\g$ be the maximal Lie algebra quotient of $\g\tp \g$. We prove that this particular Lie algebra is an abelian extension of the Lie algebra version of the nonabelian tensor product $\g \bt \g $ of Brown and Loday (Topology {\bf 26} (1987), 311335) constructed by Ellis (J. Pure Appl. Algebra {\bf 46} (1987), 111115 and Glasgow Math. J. {\bf 33} (1991), 101120). We compute this abelian extension and Leibniz homology of $\g\tp \g$ in the case, when $\g$ is a finite dimensional semisimple Lie algebra over a field of characteristic zero. Full text of the article:
Electronic fulltext finalized on: 6 May 2002. This page was last modified: 21 May 2002.
© 2002 Heldermann Verlag
