On Trivial Extensions and Higher Preprojective Algebras

2019/02/13 by Guo, Jin Yun
#16G20 #16G70 #16S37 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1902.04772

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 ≃Π( 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.

Related

• Poincaré duality for Koszul algebras
• On n-slice Algebras and Related Algebras
• On n-hereditary algebras and n-slice algebras
• Stably Calabi-Yau properties of derivation quotient algebras
• τ-slice algebras of n-translation algebras and quasi n-Fano algebras