Related papers: Deformed Bialgebra of Diffeomorphisms
An algebraic deformation theory of coalgebra morphisms is constructed.
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie…
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie…
Starting from generalized position operators, we derive complex and quaternionic angular momentum operators along with their commutation algebra as well. These algebras differ from the standard Hermitian ones, especially in terms of…
This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…
We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of…
In the paper a review of results for recovering of the weak equivalence principle in a space with deformed commutation relations for operators of coordinates and momenta is presented. Different types of deformed algebras leading to a space…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a noncomutative…
Dendriform algebras are certain splitting of associative algebras and arise naturally from Rota-Baxter operators, shuffle algebras and planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology…
We apply the notion of 2-extensions of algebras to the deformation theory of algebras. After standard results on butterflies between 2-extensions, we use this (2, 0)-category to give three perspectives on the deformation theory of algebras.…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…
Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of…
Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with $\delta$-structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric…
We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…
The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…