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Periodic Algebras which are Almost Koszul |
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| Authors: | Sheila Brenner Michael C R Butler Alastair D King |
| Institution: | (1) Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 3BX, U.K;(2) Mathematics Section, Abdus Salam ICTP, PO Box 586, 34100 Trieste, Italy;(3) Present address: Mathematical Sciences, University of Bath, Bath, BA2 7AY, U.K |
| Abstract: | The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such  almost Koszul algebras is developed and other examples are given. |
| Keywords: | periodic projective resolution Koszul ring Dynkin diagram trivial extension algebra preprojective algebra Yoneda algebra |
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