Related papers: Complex structure on quantum-braided planes
We introduce a class of right $H$--covariant first--order differential calculi on principal comodule algebras generated by the Durdevi\'c braiding $\sigma$ and a chosen vertical ideal. Starting from the universal calculus, a strong…
We compute the double complex of smooth complex-valued differential forms on projective bundles over and blow-ups of compact complex manifolds up to a suitable notion of quasi-isomorphism. This simultaneously yields formulas for 'all'…
In this work, we use tools from non-standard analysis to introduce infinite-dimensional quantum systems and quantum fields within the framework of Categorical Quantum Mechanics. We define a dagger compact category *Hilb suitable for the…
Quantum Lorentz groups H admitting quantum Minkowski space V are selected. Natural structure of a quantum space G = V x H is introduced, defining a quantum group structure on G only for triangular H (q=1). We show that it defines a braided…
It is shown that quantized irreducible flag manifolds possess a canonical $q$-analogue of the de Rham complex. Generalizing the well known situation for the standard Podle\'s' quantum sphere this analogue is obtained as the universal…
We develop the quantum component of Algebraic Phase Theory by showing that quantum phase, Weyl noncommutativity, and stabiliser codes arise as unavoidable algebraic consequences of Frobenius duality. Working over finite commutative…
This paper is about algebro-geometrical structures on a moduli space $\CM$ of anomaly-free BV QFTs with finite number of inequivalent observables or in a finite superselection sector. We show that $\CM$ has the structure of F-manifold -- a…
We introduce the periplectic $q$-Brauer category over an integral domain of characteristic not $2$. This is a strict monoidal supercategory and can be considered as a $q$-analogue of the periplectic Brauer category. We prove that the…
We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…
This paper focuses on the generalized version of the quantum double model on arbitrary $N$-dimensional simplicial complexes with finite local regularity. The core of our analysis is a detailed characterization of the frustration-free ground…
We provide a differential structure on arbitrary cleft extensions $B:=A^{\mathrm{co}H}\subseteq A$ for an $H$-comodule algebra $A$. This is achieved by constructing a covariant calculus on the corresponding crossed product algebra…
We show that the complex $C_\bullet X$ of rational simplicial chains on a compact and triangulated Poincar\'e duality space $X$ of dimension $d$ is an A$_\infty$ coalgebra with $\infty$ duality. This is the structure required for an…
We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum…
We construct $q$-deformations of quantum $\mathcal{W}_N$ algebras with elliptic structure functions. Their spin $k+1$ generators are built from $2k$ products of the Lax matrix generators of ${\mathcal{A}_{q,p}(\widehat{gl}(N)_c)}$). The…
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some domain in…
Given a differential graded (dg) symmetric Frobenius algebra $A$ we construct an unbounded complex $\mathcal{D}^{*}(A,A)$, called the Tate-Hochschild complex, which arises as a totalization of a double complex having Hochschild chains as…
This paper formulates a generalization of our work on quantum knots to explain how to make quantum versions of algebraic, combinatorial and topological structures. We include a description of previous work on the construction of Hilbert…
In this paper, we give explicit equations for homogeneous spaces corresponding to a rational isogeny of degree $3$. An explicit set of elliptic curves with elements of order $3$ in their Tate-Shafarevich group is constructed. Combining this…
We compute all Nichols algebras of rigid vector spaces of dimension 2 that admit a non-trivial quadratic relation.
We introduce a cotwist construction for Hopf algebroids that also entails cotwisting or `quantisation' of the base and which is dual to a previous twisting construction of P. Xu. Whereas the latter applied the construction to the algebra of…