Related papers: Duality for noncommutative frames
The binary products of right, left or double division in semigroups that are semilattices of groups give interesting groupoid structures that are in one to one correspondence with semigroups that are semilattices of groups. This work is…
We present a contravariant reflection of the compact $T_1$-spaces with arrows given by closed continuous functions into the category of bounded distributive lattices with arrows given by closed subfit morphisms. This reflection extends both…
Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…
The main result of the present paper is a construction of relative moduli spaces of stable sheaves over the stack of quasipolarized projective surfaces. For this, we use the theory of good moduli spaces, whose study was initiated by Alper.…
We study non-commutative projective lines over not necessarily algebraic bimodules. In particular, we give a complete description of their categories of coherent sheaves and show they are derived equivalent to certain bimodule species. This…
We consider a quantum group interpretation of the non-anticommutative deformations in Euclidean supersymmetric theories. Twist deformations in the corresponding superspaces and Lie superalgebras are constructed in terms of the left…
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed…
The goal of this paper is to define a notion of non-commutative Gelfand duality. Using techniques from derived algebraic geometry, we show that the category of rings is anti-equivalent to a subcategory of pre-ringed sites, inspired by…
A causal manifold $(M,\gamma)$ is a manifold $M$ endowed with a closed proper cone $\gamma$ in the tangent bundle $TM$ such that the projection $TM\to M$ is surjective when restricted to the interior of $\gamma$. Let $\lambda$ be the…
Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms.…
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric…
This paper establishes the homological and geometric foundations of non-commutative n-ary Gamma-semirings, unifying two previously distinct directions in Gamma-algebra: the derived Gamma-geometry developed for the commutative ternary case…
We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a 1-parameter noncommutative deformation to any projective rational surface with smooth anticanonical curve. The construction agrees with one…
We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to…
A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is…
Contextuality is widely regarded as a hallmark of quantum information, yet its structural origin is often obscured by probabilistic or operational formulations. In this work, we show that non-distributive orthomodular structure need not be…
In this paper we introduce a description of ordered groupoids as a particular type of double categories. This enables us to turn Lawson's correspondence between ordered groupoids and left-cancellative categories into a biequivalence. We use…
We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of…
We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C*-algebras. We present a new description of bivariant K-theory in terms of noncommutative…
Two approaches to the tangent space of a noncommutative space whose coordinate algebra is the enveloping algebra of a Lie algebra are known: the Heisenberg double construction and the approach via deformed derivatives, usually defined by…