Abstract
A multiplication on the 2D cohomological Hall algebra (CoHA) of the variety
of commuting matrices was described by Schiffman and Vasserot. This
construction can be generalised to other varieties that exist as the zero-locus
of a function on a smooth ambient variety. On the 2D CoHA of the character
variety of the fundamental group of a genus $g$ Riemann surface, we compare the
multiplication induced by the standard presentation and that of a brane tiling
presentation.
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