Related papers: The bigger Brauer group and twisted sheaves

Let $\mathbb{G}$ be a higher-rank connected semisimple Lie group with finite center and without compact factors. In any unitary representation $(\pi, \mathcal{H})$ of $\mathbb{G}$ without non-trivial $\mathbb{G}$-fixed vectors, we study the…

We describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern-Weil homomorphism to the twisted equivariant cohomology. We clarify that in order to have…

In recent work, we demonstrated that a spectral variety for the Berry connection of a 2d $\mathcal{N}=(2,2)$ GLSM with K\"ahler vacuum moduli space $X$ and abelian flavour symmetry is the support of a sheaf induced by a certain action on…

Generalized derivations, quasiderivations and quasicentroid of $3$-algebras are introduced, and basic relations between them are studied. Structures of quasiderivations and quasicentroid of $3$-Lie algebras, which contains a maximal…

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

We fit the Brauer group of a $\mu_r$-gerbe over a (possibly arbitrarily singular) stacky curve into an exact sequence and give characterizations for when it is short exact and conditions for when it splits. We also give a precise formula…

Let $X$ be a smooth variety over a field $K$ with function field $K(X)$. Using the interpretation of the torsion part of the \'etale cohomology group $H_{\text{\'et}}^2(K(X), \mathbb{G}_m)$ in terms of Milnor-Quillen algebraic $K$-group…

We consider M-theory compactified on a twisted 7-torus with fluxes when all the seven antisymmetric tensor fields in four dimensions have been dualized into scalars and thus the E_{7(7)} symmetry is recovered. We find that the…

In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a…

The study of Haeflier suggests that it is natural to regard a pseudogroup as an etale groupoid. We show that any etale groupoid corresponds to a pseudogroup sheaf, a new generalization of a pseudogroup. This correspondence is an analog of…

The faithfulness of the orthogonal group case of Brauer's representation of the Brauer centralizer algebras restricted to their Temperley-Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and…

We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference…

We continue the study of twisted automorphisms of Hopf algebras started in "Twisted automorphisms of Hopf algebras". In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra…

We classify Brauer graph algebras up to derived equivalence by showing that the set of derived invariants introduced by Antipov is complete. These algebras first appeared in representation theory of finite groups and can be defined for any…

We classify dynamical twists in group algebras of finite groups. Namely, we set up a bijective correspondence between gauge equivalence classes of dynamical twists (which are solutions of a certain non-linear functional equation) and…

In this PhD thesis, we have studied certain geometric structures over Lie groupoids and differentiable stacks. This thesis is based on the work [arXiv:2103.04560, arXiv:2012.08447, arXiv:2012.08442, arXiv:1907.00375]. In [arXiv:1907.00375],…

We construct twisted $\mathcal{D}$-modules on the projective line $\mathbb{P}^1$ that are equivariant for the action of the diagonal torus subgroup of $SL_2$. In the most interesting case these arise as extensions from local systems on…

We study twisted bialgebras and double twisted bialgebras, that is to say bialgebras in the category of linear species, or in the category of species in the category of coalgebras. We define the notion of cofree twisted coalgebra and…

The interplay between derivations and algebraic structures has been a subject of significant interest and exploration. Inspired by Yau's twist and the Leibniz rule, we investigate the formal deformation of twisted Lie algebras by invertible…

We develop a operator algebraic model for twisted $K$-theory, which includes the most general twistings as a generalized cohomology theory (i.e. all those classified by the unit spectrum $bgl_1(KU)$). Our model is based on strongly…