Related papers: On cyclotomic schemes over finite near-fields

We study cyclotomic association schemes over a finite commutative ring $R$ with identity. The main interest for us is to identify the normal cyclotomic schemes $C$, i.e. those for which $Aut(C)$ is a subgroup of the one-dimensional affine…

In this paper, we obtain classification results for higher-dimensional analogues of classical association schemes called association schemes on triples (ASTs). We present an algorithm that enumerates all ASTs on a fixed number of vertices…

Using cyclotomic classes of order twelve for certain finite fields, we construct an infinite family of almost difference sets and normally regular graphs applying the theory of cyclotomy. We show that in each of these fields neither the…

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence…

We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…

Let $G$ be a connected Lie group, $C$ be the maximal compact connected subgroup of the center of $G$, and let Aut$(G)$ denote the group of Lie automorphisms of $G$, viewed, canonically, also as a subgroup of GL$(\frak G)$, where $\frak G$…

In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a $C(K)$ must be nontrivial on a subspace isomorphic to $c_0$. We conclude the paper with a few examples…

We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant…

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov's…

Let $G$ be a finite group and $\mathcal{C}$ a normal subset of $G$. The Gill-Guillot graph has vertices $\mathcal C$ and $x, y \in \mathcal C$ are adjacent if and only if $x$ and $y$ commute and $\{xy^{-1},x^{-1}y\} \cap \mathcal C$ is…

With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by…

For any finite group $G$, and any positive integer $n$, we construct an association scheme which admits the diagonal group $D_n(G)$ as a group of automorphisms. The rank of the association scheme is the number of partitions of $n$ into at…

An infinite family of association schemes obtained from the general unitary groups acting transitively on the sets of isotropic vectors in the finite unitary spaces are investigated. We compute the parameters and determine the character…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

We determine all irreducible representations of primary quasi-cyclotomic fields in this paper. The methods can be applied to determine the irreducible representations of any quasi-cyclotomic field. We also compute the Artin L-functions for…

This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this problem involves transporting (near-)field structures via…

The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit…

Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed…

Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…