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## Abstract / Description of output

We introduce and study a fermionization procedure for the cohomological Hall algebra HΠQ 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 work of Etingof and Rains, via deformed dimensional reduction.

Via the same techniques, we determine the Borel-Moore homology of the stack of representations of the μ-deformed preprojective algebra introduced by Crawley-Boevey and Holland, for all dimension vectors. This provides a common generalisation of the results of Crawley-Boevey and Van den Bergh on the cohomology of smooth moduli schemes of representations of deformed preprojective algebras, and my earlier results on the Borel-Moore homology of the stack of representations of the undeformed preprojective algebra.

Via the same techniques, we determine the Borel-Moore homology of the stack of representations of the μ-deformed preprojective algebra introduced by Crawley-Boevey and Holland, for all dimension vectors. This provides a common generalisation of the results of Crawley-Boevey and Van den Bergh on the cohomology of smooth moduli schemes of representations of deformed preprojective algebras, and my earlier results on the Borel-Moore homology of the stack of representations of the undeformed preprojective algebra.

Original language | English |
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Number of pages | 22 |

Journal | Glasgow Mathematical Journal |

Publication status | Accepted/In press - 10 Feb 2022 |

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Dive into the research topics of 'A boson-fermion correspondence in cohomological Donaldson-Thomas theory'. Together they form a unique fingerprint.## Projects

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