Related papers: A condition for cyclic algebras to be split
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Splint is a decomposition of root system into union of root systems. Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching…
A calcular algebra is a subalgebra of $H^\infty(\Omega)$ with norm given by $\| \phi \| = \sup \| \phi(T) \|$ as $T$ ranges over a given class of commutative $d$-tuples of operators with Taylor spectrum in $\O$. We discuss what algebras…
In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…
For a restricted Lie algebra $L$, the conditions under which its restricted enveloping algebra $u(L)$ is semiperfect are investigated. Moreover, it is proved that $u(L)$ is left (or right) perfect if and only if $L$ is finite-dimensional.
The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair…
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…
We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial $f$ of degree $d$, there are exactly $2^{d-1}$ distinct degree $d$ polynomials with the same set of cyclic resultants as $f$.…
We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two 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…
In this paper, we examine a time-dependent family of two-dimensional algebras. We investigate the conditions under which any two algebras from this family, formed at different times, are isomorphic. Our findings reveal that the flow…
Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.
We show that for each \ell\geq 4 every sufficiently large oriented graph G with \delta^+(G), \delta^-(G) \geq \lfloor |G|/3 \rfloor +1 contains an \ell-cycle. This is best possible for all those \ell\geq 4 which are not divisible by 3.…
Let $D=(V,A)$ be a directed graph of order $n\geq 6$. Let $W$ be a subset of $V$ with $|W|\geq 6$. Suppose that every vertex of $W$ has degree at least $(3n-3)/2$ in $D$. Then for any integer partition $|W|=n_1+n_2$ with $n_1\geq 3$ and…
We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also obtain new results on irrationality and $mathbb{Q}$-linear…
Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise naturally in the context of simple affine group schemes of type $F_4$, $E_6$, or $E_7$. We…
If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already…