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On Trivial Extensions and Higher Preprojective Algebras

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arxiv 1902.04772 v1 pith:X2HAZH6U submitted 2019-02-13 math.RT math.RA

Jin Yun Guo This is my paper · ORCID
classification math.RTmath.RA
keywords algebraslambdaalgebradualpreprojectivequadratictrivialapplied
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abstract

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

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  1. Exact Hochschild extensions and deformed Calabi-Yau completions

    math.RA 2019-09 conditional novelty 7.0 of 10

    The Koszul dual of an exact Hochschild extension of a dg algebra is isomorphic to the deformed Calabi-Yau completion of the Koszul dual.

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