A fermionization procedure for the cohomological parity of representations of preprojective algebras

A boson-fermion correspondence in cohomological Donaldson-Thomas theory

We introduce and study a fermionization procedure for the cohomological hallalgebra of representations of a preprojective algebra, that selectively switches the cohomological parity of the bps lie algebra from even to odd.We do so by determining the cohomological donaldson--thomas invariants of central extensions of preprojective algebras studied in the workof etingof and rains via deformed dimensional reduction.Via the same techniques, we determine the borel-moore homology of the stack of representations of the preprojective algebra introduced by crawley-boevey and holland, for all dimension vectors.