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arXiv · 1902.04772

On Trivial Extensions and Higher Preprojective Algebras

Jin Yun Guo
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Abstract

In this paper, we show that for a Koszul $n$-homogeneous algebra $Λ$, the quadratic dual of certain twisted trivial extension is the $(n+1)$-preprojective algebra of its quadratic dual, that is, $ (Δ_νΛ)^{!,op} \simeqΠ( Λ^{ !, op })$. This is applied to the $τ$-slice algebras of stable $n$-translation algebras and gives a noncommutative version of Bernstein-Gelfand-Gelfand correspondence for such algebras.

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BibTeXRIS

Jin Yun Guo. 2019-02-13. On Trivial Extensions and Higher Preprojective Algebras. https://arxiv.org/abs/1902.04772

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