Related papers: An elementary method to compute the algebra genera…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
We identify and study a matrix algebra consisting of Pascal-type matrices. The generator of the matrix algebra is shown to well define a canonical bundle map, called the Pascal map on jet bundles, and we use it to give an intrinsic…
The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$ generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all traces of products of generic matrices, $n,d\geq 2$. It is known that over a field of…
Every commuting set of normal matrices with entries in an AW*-algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to…
Based on the tetrahedral Zamolodchikov algebra, we prove the Yang-Baxter equation for the R-matrix of 1-D SU(n) Hubbard model. Furthermore, we present a generalization of the model.
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
We give the explicit formula of the universal $R$-matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type ${\mathrm{A}}_1^{(1)}$. For $N$ with $q_{00}q_{01}$ being a primitive $N$-th root of unity,…
In this note, we study possible $\mathcal{R}$-matrix constructions in the context of quiver Yangians and Yang-Baxter algebras. For generalized conifolds, we also discuss the relations between the quiver Yangians and some other Yangian…
Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection…
We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.
We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew…
Take $A$ to be a regular quadratic algebra of global dimension three. We observe that there are examples of $A$ containing a dimension three regular cubic algebra $C$. If $B$ is another dimension three regular quadratic algebra, also…
For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existence results in certain cases: unimodular solvable Lie algebras…
Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial…
A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and…
The algebraic geometry of a universal algebra $\mathbf{A}$ is defined as the collection of solution sets of term equations. Two algebras $\mathbf{A}_1$ and $\mathbf{A}_2$ are called algebraically equivalent if they have the same algebraic…
We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we…
The $n$-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of $n$-slice algebras via their $(n+1)$-preprojective algebras and the trivial…
Bell and Zhang have shown that if $A$ and $B$ are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the…