Cluster categories coming from cyclic posets

TL;DR

This paper introduces a construction linking cyclic posets to Frobenius categories, generalizing known cluster categories and producing new examples like m-cluster categories of type A-infinity.

Contribution

It establishes that cyclic posets can generate Frobenius categories over any discrete valuation ring, broadening the scope of cluster category constructions.

Findings

Cyclic posets induce Frobenius categories over discrete valuation rings.

The construction includes known continuous cluster categories as special cases.

Twisting by automorphisms yields new cluster categories such as m-cluster categories.

Abstract

Cyclic poset are generalizations of cyclically ordered sets. In this paper we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The continuous cluster categories of arXiv:1209.1879 are examples of this construction. If we twist the construction using an admissible automorphism of the cyclic poset, we generate other examples such as the m-cluster category of type A-infinity (m>2).