Related papers: Twisted separability for adjoint functors
We use \cite{G} to study the algebra structure of twisted cotriangular Hopf algebras ${}_J\mathcal{O}(G)_{J}$, where $J$ is a Hopf $2$-cocycle for a connected nilpotent algebraic group $G$ over $\mathbb{C}$. In particular, we show that…
If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain…
It is shown that an anisotropic orthogonal involution in characteristic two is totally decomposable if it is totally decomposable over a separable extension of the ground field. In particular, this settles a characteristic two analogue of a…
An adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories. We describe the reflexive complexes and interpret the achieved results…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
We show that the Green biset functor $R_{\mathbb{C}}$ of complex characters over $\mathbb{Z}$, is not separable, i.e. it is not projective as a bimodule over itself. Also, we show that $RB_G$, the Burnside biset functor shifted by a finite…
A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points defined by the likelihood equations. We…
The Fourier(-Stieltjes) algebras on locally compact groups are important commutative Banach algebras in abstract harmonic analysis. In this paper we introduce a generalization of the above two algebras via twisting with respect to…
Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
An equivariant version of the twisted inverse pseudofunctor is defined, and equivariant versions of some important properties, including the Grothendieck duality of proper morphisms and flat base change are proved. As an application, a…
We present a geometric construction of push-forward maps along projective morphisms for cohomology theories representable in the stable motivic homotopy category assuming that the element corresponding to the stable Hopf map is inverted in…
In this paper we show that a split central simple algebra with quadratic pair which decomposes into a tensor product of quaternion algebras with involution and a quaternion algebra with quadratic pair is adjoint to a quadratic Pfister form.…
This paper constructs derived autoequivalences of Gorenstein orders as twists around spherical functors. More precisely, given a Gorenstein order $A$ and a quotient $p \colon A \to B$, then we specify natural conditions on $B$ under which…
This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtained by the theory of strict polynomial functors initiated by…
In this paper, we introduce twisted relative Rota-Baxter operators on a Leibniz algebra as a generalization of twisted Poisson structures. We define the cohomology of a twisted relative Rota-Baxter operator $K$ as the Loday-Pirashvili…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators…
We consider a generalisation of the Majid's mirror product of a Hopf algebra H, when one of the components of the product is replaced by a twist. This leads to a new "twisted mirror product" construction for cocycle bicrossproduct Hopf…
Non-commutative connections of the second type or hom-connections and associated integral forms are studied as generalisations of right connections of Manin. First, it is proven that the existence of hom-connections with respect to the…
In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of…