Frontiers of Mathematics in China >
Path A∞algebras of positively graded quivers
Received date: 18 Nov 2016
Accepted date: 13 Apr 2017
Published date: 12 Jan 2018
Copyright
Let A be a path A∞-algebra over a positively graded quiver Q. We prove that the derived category of A is triangulated equivalent to the derived category of kQ, which is viewed as a DG algebra with trivial differential. The main technique used in the proof is Koszul duality for DG algebras.
Key words： A∞-algebras; Koszul dual; DG-algebras
Hao SU . Path A∞algebras of positively graded quivers[J]. Frontiers of Mathematics in China, 2018 , 13(1) : 173 -185 . DOI: 10.1007/s11464-017-0647-y
| 1 |
Félix Y, Halperin S, Thomas J C. Rational Homotopy Theory. New York: Springer-Verlag, 2001
|
| 2 |
He J W, Lu D M. Higher Koszul algebras and A-infinity algebras. J Algebra, 2005, 293(2): 335–362
|
| 3 |
Kadeishvili T V. The algebraic structure in the homology of an A(∞)-algebra. Soobshch Akad Nauk Gruzin SSR, 1982, 108(2): 249–252
|
| 4 |
Keller B. Deriving DG categories. Ann Sci Éc Norm Supér (4), 1994, 27(1): 63–102
|
| 5 |
Keller B. Introduction to A-infinity algebras and modules. Homology, Homotopy Appl, 2001, 3(1): 1–35
|
| 6 |
Lefevre-Hasegawa K. Sur les A∞-catégories. Thèse de doctorat, Université Paris XII, 2005, http://www.math.jussieu.fr/˜keller/lefevre/publ.html
|
| 7 |
Loday J L, Vallette B. Algebraic operads. Heidelberg: Springer, 2012
|
| 8 |
Lu D M, Palmieri J H, Wu Q S, Zhang J J. A∞-algebras for ring theorists. Algebra Colloq, 2004, 11(1): 91–128
|
| 9 |
Lu D M, Palmieri J H, Wu Q S, Zhang J J. Koszul equivalences in A∞-algebras. New York J Math, 2008, 14: 325–378
|
| 10 |
Lunts V A. Formality of DG algebras (after Kaledin). J Algebra, 2010, 323(4): 878–898
|
| 11 |
Stasheff J D. Homotopy associativity of H-spaces. I. Trans Amer Math Soc, 1963, 108: 275–292
|
| 12 |
Stasheff J D. Homotopy associativity of H-spaces. II. Trans Amer Math Soc, 1963, 108: 293–312
|
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