Derivations,Central Extensions and Automorphisms of a Lie Algebra
Shou Lan GAO Department of Mathematics,Huzhou Teachers College,Huzhou 313000,P.R.China Cui Po JIANG Ye Feng PEI Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,P.R.China
We study the derivations,central extensions and the automorphisms of an infinite-dimensional Lie algebra W which appeared in the literature.Firstly,the universal central extension of W is given by calculating the second cohomology group with trivial coefficients for W.Secondly,the derivation algebra of W is determined and it is proved that W has only one outer derivation.Finally,the structures of the automorphism groups of W and its universal central extension are characterized.
Shou Lan GAO Department of Mathematics,Huzhou Teachers College,Huzhou 313000,P.R.China Cui Po JIANG Ye Feng PEI Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,P.R.China.
Derivations,Central Extensions and Automorphisms of a Lie Algebra. Acta Mathematica Sinica, Chinese Series, 2009(02): 75-82 https://doi.org/10.12386/A2009sxxb0033
