Related papers: Duality for action bialgebroids
We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras $H$ and those for cocycle twists $H^{\sigma}$ of $H$. This implies an equivalence between modules…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
This is a slightly corrected version of the article published by Functional Analysis and its Applications in 1993. We define the quadratic duality for algebras with nonhomogeneous relations; the duality between the algebra of differential…
In this paper we mainly construct bicrossproduct for finite-dimensional monoidal Hom-Hopf algebra $(H,\alpha)$, generalizing the Majid's bicrossproduct. Naturally the Hom-type bicrossproduct leads to Drinfel'd double $(H^{op}\bowtie…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of 'doubled kets' (i.e. mixing), and by tracing out part of a 'doubled' two-system ket (i.e. dilation). Both…
A DFT algebroid is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a DFT algebroid is a structure defined on a vector bundle over doubled…
D-brane actions depend on a world-volume abelian vector field and are described by Born-Infeld-type actions. We consider the vector field duality transformations of these actions. Like the usual 2d scalar duality rotations of isometric…
Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…
In string theory it is known that abelian isometries in the sigma model lead to target space duality. We generalize this duality to backgrounds with non--abelian isometries. The procedure we follow consists of gauging the isometries of the…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
It has been speculated in the literature that the effective actions of string theories at any order of $\alpha'$ should be invariant under the Buscher rules plus their higher covariant derivative corrections. This may be used as a…
It is proven that a matched pair of actions on a Hopf algebra $H$ is equivalent to the datum of a Yetter-Drinfeld brace, which is a novel structure generalising Hopf braces. This improves a theorem by Angiono, Galindo and Vendramin,…
We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra $H$ associated to the factorization of a finite group into two subgroups. The representations of the quantum double…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of `doubled kets' (i.e. mixing), and by tracing out part of a `doubled' two-system ket (i.e. dilation). Both…
The structure of filtered algebras of Grothendieck's differential operators of truncated polynomials in one variable and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality…
The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true, and continue to explore…
We develop a tensor categorical duality in the sprit of the Tannaka-Krein duality for the C*-algebras admitting the Yetter-Drinfeld module structure over a compact quantum group. Under this duality, given a reduced compact quantum group G,…
We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve module algebras that are Koszul, in which case a PBW theorem we established…