On homology of Lie algebras over commutative rings

Ivanov, Sergei O.; Pavutnitskiy, Fedor; Romanovskii, V. R.; Zaikovskii, Anatolii

doi:10.1016/j.jalgebra.2021.06.019

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“…However, in view of a better understanding of the (weak) categorical minor theorem, it would be interesting to investigate also further cohomology theories of graphs, quivers and categories. To name a few, some recent intriguing examples, related to magnitude homology, are for example reachability homology [HR23,CR23], spectral homology [Iva23], or those introduced in [IP23,Rof23].…”

Section: Introductionmentioning

confidence: 99%

Combinatorial and topological aspects of path posets, and multipath cohomology

2022

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Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets and to provide computational tools for multipath cohomology. In particular, we develop acyclicity criteria and provide computations of multipath cohomology groups of oriented linear graphs. We further interpret the path poset as the face poset of a simplicial complex, and we investigate realisability problems.

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Section: Introductionmentioning

confidence: 99%