相关论文: Norton algebras of the Hamming Graphs via linear c…
A Norton algebra is an eigenspace of a distance regular graph endowed with a commutative nonassociative product called the Norton product, which is defined as the projection of the entrywise product onto this eigenspace. The Norton algebras…
We consider the Norton algebra associated with a $Q$-polynomial primitive idempotent of the adjacency matrix for a distance-regular graph. We obtain a formula for the Norton algebra product that we find attractive.
To each of the Johnson, Grassmann and Hamming graphs we associate a lattice and characterize the eigenspaces of the adjacency operator in terms of this lattice . We also show that each level of the lattice induces in a natural way a tight…
Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…
We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces $\{X(m,n)\}_{m,n=0}^\infty$ equipped…
Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…
This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…
In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into…
The principal observation of the present paper is that an inner isotopy (i.e. a principal isotopy defined by an algebra endomorphism) is a very helpful instrument in constructing and studying interesting classes of nonassociative algebras.…
We show that the infinite symmetric product of a connected graded-commutative algebra over the rationals is naturally isomorphic to the free graded-commutative algebra on the positive degree subspace of the original algebra. In particular,…
We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on…
We consider the algebra $A_N=k\langle x, y\rangle/(yx-xy-x^N)$, with $k$ a field of characteristic zero and $N$ a positive integer. Our main result is a complete description of the first Hochschild cohomology $\operatorname{HH}^1(A_N)$ of…
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…
A null vector is an algebraic quantity with square equal to zero. I denote the universal algebra generated by taking all sums and products of null vectors over the real or complex numbers by N. The rules of addition and multiplication in N…
We give a construction that takes a simple linear algebraic group $G$ over a field and produces a commutative, unital, and simple non-associative algebra $A$ over that field. Two attractions of this construction are that (1) when $G$ has…
Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…
Let $\mathbf D$ be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On $\BZ\mathbf D$ we define a product and a coproduct, together with an internal product, that is,…
The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined analogously to the sectional curvature of a pseudo-Riemannian metric, with the associator in place of the Levi-Civita covariant…
A Hom-type generalization of non-commutative Poisson algebras, called non-commutative Hom-Poisson algebras, are studied. They are closed under twisting by suitable self-maps. Hom-Poisson algebras, in which the Hom-associative product is…
We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…