Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry

By M. Kontsevich, Y. Soibelman. 2008

294 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/85a99720c010d694a087567589354d610918d442

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Citations in the corpus

Triangulated Categories: Cluster algebras, quiver representations and triangulated categories (2008, unknown): “The main ingredient of the proof of this theorem is the construction of a ‘minimal model’, which, in a different language, was also obtained in [84] and [ 99 ].”
Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “For more background material concerning A∞bimodules, see [50, 24, 22, 25, 41].”
Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie (2006, methodology): “In this paper, we prefer to use the second possibility, which is closer to the way the degeneration conjecture has been formulated in [ KS ].”
Calabi–Yau triangulated categories (2008, background): “5.2. Cyclic structures and potentials. We follow section 10 of [ 42 ].”
Batalin-Vilkovisky algebra structures on Hochschild Cohomology (2007, unknown): “In [20] or [28, Corollary 3.4] or [5, Section 1.4] or [21, Theorem B] or [ 22, Section 11.6 ] or [18], this Batalin-Vilkovisky algebra structure on HH (A;A) extends to a structure of algebra on the Hochschild cochain complexC (A;A) over various operads or PROPs: the so-called cyclic Deligne conjectu”
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations (2008, background): “Recall (see [41], [ 42 ]) that the deformation theory of any object E ∈ Ob(C) is controlled by a differential-graded Lie algebra (DGLA for short) gE such that Hi(gE) ≃ Exti(E, E), i ∈ Z. For a given Schur object E instead of gE we can use a”