Recall that using the Levi-Cevita symbol the determinant can be written as $$\operatorname{det} A=\frac{1}{n!}\epsilon_{i_1\dots i_n}\epsilon_{j_1\dots j_n}A_{i_1j_1}\dots A_{i_nj_n}$$ Some computations that I do recently turned out to produce objects of the type
$$\epsilon_{i_1\dots i_n}\epsilon_{j_1\dots j_n}\epsilon_{k_1\dots k_n}\epsilon_{l_1\dots l_n}T_{i_1j_1k_1l_1}\dots T_{i_nj_nk_nl_n}$$ which look like a freshmen-style generalization of determinant to tensors. In my computations only even-rank tensors appear.
Is there a name for such things? Do they have any interesting properties?
