Related papers: On Integro-Differential Algebras
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
The purpose of the present paper is to investigate cohomologies and deformations of weighted Rota-Baxter Lie algebras as well as weighted Rota-Baxter associative algebras with derivations. First we introduce a notion of weighted Rota-Baxter…
An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying…
A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…
We determine the Krull-Gabriel dimension of weighted surface algebras, a class of algebras which recently appeared in the context of classification of tame symmetric periodic algebras of non-polynomial growth. Moreover, we consider…
A Rota--Baxter operator is an algebraic abstraction of integration, which is the typical example of a weight zero Rota-Baxter operator. We show that studying the modules over the polynomial Rota--Baxter algebra $(k[x],P)$ is equivalent to…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials ($p > 1$). We study…
We consider the cotriple resolution of algebras over operads in differential graded modules. We focus, to be more precise, on the example of algebras over the differential graded Barratt-Eccles operad and on the example of commutative…
Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial…
The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are…
We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic…
A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct the monomial basis of the free special Gelfand-Dorfman…
Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…
In the context of commutative differential graded algebras over $\mathbb Q$, we show that an iteration of "odd spherical fibration" creates a "total space" commutative differential graded algebra with only odd degree cohomology. Then we…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted…
Assume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital algebra map from the homology of the DGA to its…
We study a partial differential relation that arises in the context of the Born-Infeld equations (an extension of the Maxwell's equations) by using Gromov's method of convex integration in the setting of divergence free fields.