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We study a semisimple extension of a Takiff superalgebra, which turns out to have a remarkably rich representation theory. We determine the blocks in both the finite-dimensional and BGG module categories and also classify the Borel subalgebras. We further compute all extension groups between two finite-dimensional simple objects and prove that all non-principal blocks in the finite-dimensional module category are Koszul.

Representation Theory of a Semisimple Extension of the Takiff Superalgebra