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A A BV algebra and a QP-structure of degree 3 is formulated. A QP-structureof degree 3 gives rise to Lie algebroids up to homotopy and its algebraic andgeometric structure is analyzed. A new algebroid is constructed, which derivesa new topological field theory in 4 dimensions by the AKSZ construction.

QP-Structures of Degree 3 and 4D Topological Field Theory