Yoneda algebras of almost Koszul algebras

Zheng, Lan

doi:10.1007/s12044-015-0248-1

Proc Math Sci

2015

DOI: 10.1007/s12044-015-0248-1

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Yoneda algebras of almost Koszul algebras

Lan Zheng

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2018

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Koszul duality and the PBW theorem in symmetric tensor categories in positive characteristic

Etingof

2018

Advances in Mathematics

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We generalize the theory of Koszul complexes and Koszul algebras to symmetric tensor categories. In characteristic zero the generalization is routine, while in characteristic p there is a subtlety -the symmetric algebra of an object is not always Koszul (i.e., its Koszul complex is not always exact). Namely, this happens in the Verlinde category Ver p in any characteristic p ≥ 5. We call an object Koszul if its symmetric algebra is Koszul, and show that the only Koszul objects of Ver p are usual supervector spaces, i.e., a non-invertible simple object L m (2 ≤ m ≤ p− 2) is not Koszul. We show, however, that the symmetric algebra SL m is almost Koszul in the sense of Brenner, Butler and King (namely, (p − m, m)-Koszul), and compute the corresponding internal Yoneda algebra (i.e., the internal Ext-algebra from the trivial module to itself).We then proceed to discuss the PBW theorem for operadic Lie algebras (i.e., algebras over the operad Lie).

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Koszul duality and the PBW theorem in symmetric tensor categories in positive characteristic

Etingof

2018

Advances in Mathematics

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Yoneda algebras of almost Koszul algebras

Cited by 1 publication

References 6 publications

Koszul duality and the PBW theorem in symmetric tensor categories in positive characteristic

Koszul duality and the PBW theorem in symmetric tensor categories in positive characteristic

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