Related papers: Braid action on derived category of Nakayama algeb…

The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization…

A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a…

We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical…

We discuss an action of the Grothendieck-Teichm\"{u}ller proalgebraic group on the linear span of proalgebraic tangles, oriented tangles completed by a filtration of Vassiliev. The action yields a motivic structure on tangles. We derive…

We give a geometric description of the blocks of the Brauer algebra $B_n(\delta)$ in characteristic zero as orbits of the Weyl group of type $D_n$. We show how the corresponding affine Weyl group controls the representation theory of the…

This article surveys many standard results about the braid group with emphasis on simplifying the usual algebraic proofs. We use van der Waerden's trick to illuminate the Artin-Magnus proof of the classic presentation of the algebraic…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

Suppose that $(G,T)$ is a second countable locally compact transformation group given by a homomorphism $\ell:G\to\Homeo(T)$, and that $A$ is a separable continuous-trace \cs-algebra with spectrum $T$. An action $\alpha:G\to\Aut(A)$ is said…

Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal…

We show that no finite index subgroup of a sufficiently complicated mapping class group or braid group can act faithfully by $C^{1+\mathrm{bv}}$ diffeomorphisms on the circle, which generalizes a result of Farb-Franks, and which parallels a…

We construct an infinite tower of irreducible calibrated representations of periplectic Brauer algebras on which the cup-cap generators act by nonzero matrices. As representations of the symmetric group, these are exterior powers of the…

There is a natural action of the braid group on the symmetric matrices with units on the diagonal, appearing in various fields as Singularity Theory, Frobenius Manifolds or Isomonodromic deformations of certain classes of linear…

We prove that the Nakayama automorphism of a Frobenius algebra acts trivially on the Hochschild cohomology of the algebra. As an application of this fact, we show how to construct certain invariants attached to such algebras, and to their…

Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by…

Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible varieties over a finitely generated field $k$ such that the generic fiber $X$ is smooth, projective and geometrically connected. Assuming that $C$ is a curve…

A class of subgroups is obtained for symmetric groups using signed Brauer diagrams.

To any Frobenius superalgebra $A$ we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer category. We define natural actions of these categories on categories of supermodules for general linear Lie…

In this paper we prove an analogue of Brauer's theorem for faithful objects in fusion categories. Other notions, such as the order and the index associated to faithful objects of fusion categories are also discussed. We show that the index…

Motivated by the Brou\'e conjecture on blocks with abelian defect groups for finite reductive groups, we study "parabolic" Deligne-Lusztig varieties and construct on those which occur in the Brou\'e conjecture an action of a braid monoid,…

The correspondence between the braid group on a solid torus of arbitrary genus and the algebra of Yang-Baxter and reflection equation operators is shown. A representation of this braid group in terms of $R$-matrices is given. The…