Related papers: Set of evolution operators of an evolution algebra
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…
In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, we provide four different constructions producing three-dimensional evolution algebras from…
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
We introduce an (evolution) algebra identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. The basic properties of the algebra are studied. We prove that this algebra is commutative…
The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras…
This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial…
The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. For such algebras in terms of its structure constants we…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
We consider the endomorphism operad of a functor, which is roughly the object of natural transformations from (monoidal) powers of that functor to itself. There are many examples from geometry, topology, and algebra where this object has…
Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects then Hamiltonians. In this paper we study an evolution operator for the one-dimensional integrable q-deformed Bose gas with…
We prove that every automorphism of an infinite-dimensional vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are the product of three…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra of evolutionary vector fields of the jet space are subject to…
Let A be an evolution algebra (possibly infinite-dimensional) equipped with a fixed natural basis B, and let E be the associated graph defined by Elduque and Labra. We describe the group of automorphisms of A that are diagonalizable with…
This paper describes work carried out on a model for the evolution of graph classes in complex objects. By defining evolution rules and propagation strategies on graph classes, we aim to define a user-definable means to manage data…
In this work we study the space of derivations of non-degenerate evolution algebras. We improve some results obtained recently in the literature and, as a consequence, we advance in the description of the derivations for $n$-dimensional…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…