On central extensions of simple differential algebraic groups

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We consider central extensions Z E G in the category of linear differential algebraic groups. We show that if G is simple non-commutative and Z is unipotent with the differential type smaller than that of G, then such an extension splits. We also give a construction of central extensions illustrating that the condition on differential types is important for splitting. Our results imply that non-commutative almost simple linear differential algebraic groups, introduced by Cassidy and Singer, are simple.