Local Automorphisms and Local Superderivations of Model Filiform Lie Superalgebras

In this paper, we give the forms of local automorphisms (resp. superderivations) of model filiform Lie superalgebra <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi>L</a:mi></a:mrow><a:mrow><a:mi>n</a:mi><a:mo>,</a:mo><a:mi>m</a:mi></a:mrow></a:msub></a:math> in the matrix version. Linear 2-local automorphisms (resp. superderivations) of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:msub><c:mrow><c:mi>L</c:mi></c:mrow><c:mrow><c:mi>n</c:mi><c:mo>,</c:mo><c:mi>m</c:mi></c:mrow></c:msub></c:math> are also characterized. We prove that each linear 2-local automorphism of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"><e:msub><e:mrow><e:mi>L</e:mi></e:mrow><e:mrow><e:mi>n</e:mi><e:mo>,</e:mo><e:mi>m</e:mi></e:mrow></e:msub></e:math> is an automorphism.