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arXiv · 1607.02473

$τ$-Tilting Theory and $τ$-Slices

Hipolito Treffinger
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Abstract

Comparing the module categories of an algebra and of the endomorphism algebra of a given support $τ$-tilting module, we give a generalization of the Brenner-Butler's tilting theorem in the framework of $τ$-tilting theory. Afterwards we define $τ$-slices and prove that complete slices of tilted algebras and local slices of cluster tilted algebras are examples of complete $τ$-slices. Then we apply this concept to the study of simply connected tilted algebras. Finally, we study the one-point extensions and the split-by-nilpotent extensions of an algebra with $τ$-slices.

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BibTeXRIS

Hipolito Treffinger. 2016-07-08. $τ$-Tilting Theory and $τ$-Slices. https://doi.org/10.1016/j.jalgebra.2017.03.004

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