arXiv subjects

Kunio Yamagata

Publications and source records attributed to Kunio Yamagata.

4 recordsLinked to original sources

arXiv2021

Socle equivalences of weighted surface algebras

We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field $K$ which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in Erdmann and Skowroński (J. Algebra 544:170-227, 2020). In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4.

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arXiv2019

Socle deformations of selfinjective orbit algebras of tilted type

We survey recent development of the study of finite-dimensional selfinjective algebras over a field which are socle equivalent to selfinjective orbit algebras of tilted type.

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arXiv2018

Self-injective algebras with hereditary stable slice

We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.

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arXiv2017

Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension

A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms of extensions and of Hochschild cohomology, and finiteness in general is derived from homological conjectures. Then invariance under stable equivalences is shown to hold, with some exceptions when there are nodes in case of additive equivalences, and without exceptions in case of triangulated equivalences. Stable equivalences of Morita type and derived equivalences, both between self-injective algebras, are shown to preserve rigidity dimension as well.

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