  We introduce the marked Brauer algebra and the marked Brauer category. These
generalize the analogous constructions for the ordinary Brauer algebra to the
setting of a homogeneous bilinear form on a $\mathbb{Z}_2$-graded vector space.
We classify the simple modules of the marked Brauer algebra over any field of
characteristic not two. Under suitable assumptions we show that the marked
Brauer algebra is in Schur-Weyl duality with the Lie superalgebra,
$\mathfrak{g}$, of linear maps which leave the bilinear form invariant. We also
provide a classification of the indecomposable summands of the tensor powers of
the natural representation for $\mathfrak{g}$ under those same assumptions. In
particular, our results generalize Moon's work on the Lie superalgebra of type
$\mathfrak{p}(n)$ and provide a unifying conceptual explanation for his
results.
