相关论文: Non-commutative association schemes and their fusi…
We can obtain a non-symmetric class $2$ association scheme by a skew-Hadamard matrix. We begin with a skew-Hadamard matrix of order $n$, construct a skew-Hadamard matrix of order $2n$ by doubling construction, and a non-symmetric class $2$…
Divisible design digraphs are constructed from skew balanced generalized weighing matrices and generalized Hadamard matrices. Commutative and non-commutative association schemes are shown to be attached to the constructed divisible design…
In this paper we aim to characterize association schemes all of whose symmetric fusion schemes have only integral eigenvalues, and classify those obtained from a regular action of a finite group by taking its orbitals.
Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are…
In this paper we show that for any fusion $\mathcal{B}$ of an association scheme $\mathcal{A}$, the generalized Hamming scheme $H(n,\mathcal{B})$ is a nontrivial fusion of $H(n,\mathcal{A})$. We analyze the case where $\mathcal{A}$ is the…
We provide a method to construct $t$-designs from weighing matrices and association schemes. One instance of our method can produce a $3$-design from any (symmetric or skew-symmetric) conference matrix, thereby providing a partial answer to…
We define Bush-type generalized Hadamard matrices over abelian groups and construct symmetric Bush-type generalized Hadamard matrices over the additive group of finite field $\mathbb{F}_q$, $q$ a prime power. We then show and study an…
We construct a pair of non-commutative rank 8 association schemes from a rank 3 non-symmetric association scheme. For the pair, two association schemes have the same character table but different Frobenius-Schur indicators. This situation…
We make an attempt to develop "noncommutative algebraic geometry" in which noncommutative affine schemes are in one-to-one correspondence with associative algebras. In the first part we discuss various aspects of smoothness in affine…
An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional…
We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for…
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (multivariate) setting. We introduce the concept of Horner…
In this article we determine feasible parameter sets for (what could potentially be) commutative association schemes with noncyclotomic eigenvalues that are of smallest possible rank and order. A feasible parameter set for a commutative…
Commutation formulae with respect to a non-symmetric affine connection are obtained in this paper. The components of commutation formulae in this paper are covariant derivatives of tensors with respect to symmetric and non-symmetric affine…
A (di)graph $\Gamma$ generates a commutative association scheme $\mathfrak{X}$ if and only if the adjacency matrix of $\Gamma$ generates the Bose-Mesner algebra of $\mathfrak{X}$. In [17, Theorem 1.1], Monzillo and Penji\'{c} proved that,…
An association scheme is called amorphic if every possible fusion of relations gives rise to another association scheme. In earlier work, we showed that if an association scheme has at most one relation that is neither strongly regular of…
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…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric…
The main purpose of this paper is to describe various phenomena and certain constructions arising in the process of studying derived noncommutative schemes. Derived noncommutative schemes are defined as differential graded categories of a…