Abstract. In his study of quantum groups, Drinfeld suggested to consider set-theoretic solutions of the Yang–Baxter equation as a discrete analogon. As a typical example, every conjugacy class in a group, or more generally every rack Q provides such a Yang–Baxter operator cQ: x ⊗ y 7 → y ⊗ x y. In this article we study deformations of cQ within the space of Yang–Baxter operators. Infinitesimally these deformations are classified by Yang–Baxter co-homology. We show that the Yang–Baxter cochain complex of cQ homotopy-retracts to a much smaller subcomplex, called quasi-diagonal. This greatly simplifies the deformation theory of cQ, including the modular case which had previously been left in suspense, by establishing that every deformation of ...
AbstractWe construct two-parameter families of integrable λ-deformations of two-dimensional field th...
This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a...
International audienceSelf-distributive (SD) structures form an important class of solutions to the ...
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a speci...
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic soluti...
AbstractLet g be a complex, semi-simple Lie algebra, h⊂g a Cartan subalgebra and D a subdiagram of t...
This paper deals with left non-degenerate set-theoretic solutions to the Yang–Baxter equation (= LND...
For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(...
Racks and quandles are fundamental algebraic structures related to the topology of knots, braids, an...
summary:The cotangent cohomology of {\it S. Lichtenbaum} and {\it M. Schlessinger} [Trans. Am. Math....
AbstractGerstenhaber and Schack [NATO Adv. Sci. Inst. Ser. C, Vol. 247, 1986] developed a deformatio...
In this paper, we study two deformation procedures for quantum groups: deformations by twists, that ...
© Astérisque 408, SMF 2019 — In this paper, we study the classical and quantum equivariant cohomolog...
In this dissertation, we developed a mathematical framework for cohomological field theories (CohFTs...
We construct two-parameter families of integrable λ -deformations of two-dimensional field theories...
AbstractWe construct two-parameter families of integrable λ-deformations of two-dimensional field th...
This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a...
International audienceSelf-distributive (SD) structures form an important class of solutions to the ...
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a speci...
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic soluti...
AbstractLet g be a complex, semi-simple Lie algebra, h⊂g a Cartan subalgebra and D a subdiagram of t...
This paper deals with left non-degenerate set-theoretic solutions to the Yang–Baxter equation (= LND...
For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(...
Racks and quandles are fundamental algebraic structures related to the topology of knots, braids, an...
summary:The cotangent cohomology of {\it S. Lichtenbaum} and {\it M. Schlessinger} [Trans. Am. Math....
AbstractGerstenhaber and Schack [NATO Adv. Sci. Inst. Ser. C, Vol. 247, 1986] developed a deformatio...
In this paper, we study two deformation procedures for quantum groups: deformations by twists, that ...
© Astérisque 408, SMF 2019 — In this paper, we study the classical and quantum equivariant cohomolog...
In this dissertation, we developed a mathematical framework for cohomological field theories (CohFTs...
We construct two-parameter families of integrable λ -deformations of two-dimensional field theories...
AbstractWe construct two-parameter families of integrable λ-deformations of two-dimensional field th...
This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a...
International audienceSelf-distributive (SD) structures form an important class of solutions to the ...