Related papers: On the deformation of path algebras
The representation and the cohomology theory of associative 2-algebras are developed. We study the deformations and abelian extensions of associative 2-algebras in details.
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
We describe the deformation cohomology of a symplectic groupoid, and use it to study deformations via Moser path methods, proving a symplectic groupoid version of the Moser Theorem. Our construction uses the deformation cohomologies of Lie…
We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…
In the framework of C*-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes' tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel's…
Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…
In this paper, we consider deformations of Lie 2-algebras via the cohomology theory. We prove that a 1-parameter infinitesimal deformation of a Lie 2-algebra $\g$ corresponds to a 2-cocycle of $\g$ with the coefficients in the adjoint…
In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full…
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.
De Broglie waves may be a reflection of a deformation inherent in the path algebra of phase space. On a Riemannian manifold equipped with a suitable 2-form, the product of paths, which is ordinarily their concatenation, can be deformed by…
The group action which defines the moduli problem for the deformation space of flat affine structures on the two-torus is the action of the affine group $\Aff(2)$ on $\bbR^2$. Since this action has non-compact stabiliser $\GL(2,\bbR)$, the…
In this paper, we give an explicit description about the second Hochschild cohomology groups of bipartite Brauer graph algebras with trivial grading. Based on this, we provide geometric interpretations of deformations associated to some…
We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward…
The Leit-Faden of the article (which is partially a survey) is a negative answer to the question whether, for a compact complex manifold which is a $K(\pi, 1)$ the diffeomorphism type determines the deformation type. We show that a…
We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…