Related papers: Novikov algebras and multi-indices in regularity s…
We establish a formal variational calculus of supervariables, which is a combination of the bosonic theory of Gel'fand-Dikii and the fermionic theory in our earlier work. Certain interesting new algebraic structures are found in connection…
We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In particular, we prove that differential algebraic dependence of a…
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…
This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by A. Connes and D. Kreimer using admissible cuts, and the second is defined by D. Calaque, K. Ebrahimi-Fard and the second author using…
We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…
The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…
We compute the truncated point schemes of subalgebras of Fomin-Kirillov algebras associated with certain graphs. While Fomin-Kirillov algebras do not admit any truncated point modules, we prove a tight bound on the degrees of truncated…
We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative (semi)prime algebra is (semi)prime algebra. We proved this…
We define a general notion of set of indices which, using concepts from pre-ordered sets theory, permits to unify the presentation of several Colombeau-type algebras of nonlinear generalized functions. In every set of indices it is possible…
We propose a natural extension of the Novikov numbers for the basic cohomology class of a closed basic $1$-form on a proper Lie groupoid of finitely generated type. As an application, we prove corresponding Novikov inequalities for compact…
In this paper, we construct a kind of infinite-dimensional Novikov algebras and give its realization by hyperbolic sine functions and hyperbolic cosine functions.
We define a class of algebras describing links of binary semi-isolating formulas on a set of realizations for a family of 1-types of a complete theory. These algebras include algebras of isolating formulas considered before. We prove that a…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
We introduce a family of maps parametrised by certain ribbon graphs. It is based on a connection in non-commutative geometry and contains the double divergence as a special case. Applying the construction to the case of the group algebra of…
In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled k-ary trees, rooted labeled…
We give a systematic construction of Hopf algebra structures on braided cofree coalgebras. The relevant underlying structures are braided algebras and braided coalgebras. We provide some interesting examples of these algebras and coalgebras…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.