Brauer–Severi motives and Donaldson–Thomas invariants of quantized threefolds

Abstract

Motives of Brauer–Severi schemes of Cayley-smooth algebras associated to homogeneous superpotentials are used to compute inductively the motivic Donaldson–Thomas invariants of the corresponding Jacobian algebras. This approach can be used to test the conjectural exponential expressions for these invariants, proposed in [3]. As an example we confirm the second term of the conjectured expression for the motivic series of the homogenized Weyl algebra.