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Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

- M. Kontsevich, Y. Soibelman
- Mathematics, Physics
- 16 November 2008

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category… Expand

Homological mirror symmetry and torus fibrations

- M. Kontsevich, Y. Soibelman
- Mathematics, Physics
- 7 November 2000

In this paper we discuss two major conjectures in Mirror Symmetry: Strominger-Yau-Zaslow conjecture about torus fibrations, and the homological mirror conjecture (about an equivalence of the Fukaya… Expand

Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants

- M. Kontsevich, Y. Soibelman
- Mathematics, Physics
- 14 June 2010

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of… Expand

Affine Structures and Non-Archimedean Analytic Spaces

- M. Kontsevich, Y. Soibelman
- Mathematics
- 28 June 2004

In this paper we propose a way to construct an analytic space over a non-archimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is… Expand

Deformations of algebras over operads and Deligne's conjecture

- M. Kontsevich, Y. Soibelman
- Mathematics, Physics
- 26 January 2000

In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces… Expand

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

- M. Kontsevich, Y. Soibelman
- Physics
- 2008

We develop a geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. The geometric approach clarifies several… Expand

Quantum affine algebras and their representations

- D. Kazhdan, Y. Soibelman
- Mathematics
- 12 May 1995

Abstract Some questions on the representation theory of quantum affine algebras are discussed from the categorical point of view.

Algebras of functions on quantum groups

- Leonid Korogodski, Y. Soibelman
- Mathematics
- 1998

Introduction Poisson Lie groups Quantized universal enveloping algebras Quantized algebras of functions Quantum Weyl group and the universal quantum $R$-matrix Bibliography.

Algebras of functions on compact quantum groups, Schubert cells and quantum tori

- S. Levendorskii, Y. Soibelman
- Mathematics
- 1 July 1991

AbstractThe structures of Poisson Lie groups on a simple compact group are parametrized by pairs (a, u), wherea∈R,
$$u \in \Lambda ^2 \mathfrak{h}_R$$
, and
$$\mathfrak{h}_R$$
is a real Cartan… Expand

Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

- M. Kontsevich, Y. Soibelman
- Mathematics, Physics
- 11 June 2006

We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several… Expand

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