Related papers: On real chains of evolution algebras
A noncommutative projective variety is defined, after Artin and Zhang, by a graded coherent algebra A, where the category of coherent sheaves is the quotient qgr(A) of the category of finitely presented graded modules by the subcategory of…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and…
A curled algebra is a non-associative algebra in which $x$ and $x^2$ are linearly dependent for every element $x$. An algebra is called endo-commutative, if the square mapping from the algebra to itself preserves multiplication. In this…
We construct a new bijection between the set of $n\times k$ $0$-$1$ matrices with no three $1$'s forming a $\Gamma$ configuration and the set of $(n,k)$-Callan sequences, a simple structure counted by poly-Bernoulli numbers. We give two…
The standard coalescent is widely used in evolutionary biology and population genetics to model the ancestral history of a sample of molecular sequences as a rooted and ranked binary tree. In this paper, we present a representation of the…
We show that for finite n at least 3, every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras, polyadic algebras, and polyadic equality algebras contains an…
Let $\{A_{i,n}\}$ be a triangular array of elements in a Banach algebra, whose norms do not grow too fast, and whose row averages converge to $A$. Let $\sigma \in S(n)$ be a permutation drawn uniformly at random. If the array only contains…
Group classification of a class of third-order nonlinear evolution equations generalizing KdV and mKdV equations is performed. It is shown that there are two equations admitting simple Lie algebras of dimension three. Next, we prove that…
We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields.…
In characteristic zero, Bezrukavnikov has shown that the category of perverse coherent sheaves on the nilpotent cone of a simply connected semisimple algebraic group is quasi-hereditary, and that it is derived-equivalent to the category of…
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…
We provide explicit formulas of non-recursive type for the linearizing transformations of a non-resonant analytic germ of diffeomorphism at a fixed point or a non-resonant analytic germ of vector field at a singular point, in any complex…
We study symplectic structures on nilpotent Lie algebras. Since the classification of nilpotent Lie algebras in any dimension seems to be a crazy dream, we approach this study in case of 2-step nilpotent Lie algebras (in this sub-case also,…
An extended free fermionic construction of the internal N=1 world sheet supercurrent for four-dimensional superstring theory is given. We show how it can describe theories with massless fermions, and we discuss the corresponding N=2…
We introduce the abstract notion of a chain, which is a sequence of $n$ points in the plane, ordered by $x$-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general…
A universal cycle for permutations of length $n$ is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length $n$, and containing all permutations of length $n$ as factors. It is well known…
We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poisson algebra over an algebraically closed field decomposes…
We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain…
A classification of all possible realizations of the Galilei, Galilei-similitude and Schroedinger Lie algebras in three-dimensional space-time in terms of vector fields under the action of the group of local diffeomorphisms of the space…