| 研究実績の概要 |
I have finished two preprints that are submitted and currently under review.
The first one is titled "Dominant Auslander-Gorenstein algebras and Koszul duality". This research studies a certain generalisation of Auslander algebra and extended the Auslander correspondence to a larger class of algebras. Moreover, we also showed that this class is closed under Koszul duality and looked at some interesting examples.
The second preprint is titled "Marked non-orientable surfaces and cluster categories via symmetric representations". We bring in new technology to extend the study of algebras associated to orientable surfaces to non-orientable ones. This research provide the first important step towards categorification of cluster algebra-like objects associated to non-orientable surfaces.
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