相关论文: The Tetrahedron algebra, the Onsager algebra, and …
Recently Terwilliger and the present author found a presentation for the three-point $\mathfrak{sl}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $\boxtimes$ by generators and relations…
We give a presentation of the universal central extension of the three-point loop algebra L over sl_2 by generators and relations. Our presentation arises from the realization of L as the tetrahedron Lie algebra and leads to connections…
In this thesis, four realizations of the Onsager algebra are explored. We begin with its original definition as introduced by Lars Onsager. We then examine how the Onsager algebra can be presented as a Lie algebra with two generators and…
The tridiagonal algebra is defined by two generators and two relations, called the tridiagonal relations. Special cases of the tridiagonal algebra include the $q$-Onsager algebra, the positive part of the $q$-deformed enveloping algebra…
Recently Brian Hartwig and the second author found a presentation for the three-point $sl_2$ loop algebra by generators and relations. To obtain this presentation they defined a Lie algebra $\boxtimes$ by generators and relations, and…
Recently B. Hartwig and the second author found a presentation for the three-point $sl_2$ loop algebra via generators and relations. To obtain this presentation they defined an algebra $\boxtimes$ by generators and relations, and displayed…
We define an $ sl(N) $ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a…
The action of the symmetric group of degree 4 on the Tetrahedron algebra, introduced by Hartwig and Terwilliger, is studied. This action gives a grading of the algebra which is related to its decomposition into a direct sum of three…
We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…
The Onsager Lie algebra $O$ is an infinite-dimensional Lie algebra defined by generators $A$, $B$ and relations $[A, [A, [A, B]]] = 4[A, B]$ and $[B, [B, [B, A]]] = 4[B, A]$. Using an embedding of $O$ into the tetrahedron Lie algebra…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of…
In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra $T$ of a distance-regular graph that has $q$-Racah type; (ii) the $q$-tetrahedron algebra $\boxtimes_q$ which is a $q$-deformation of…
We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…
In 1998, Georgia Benkart and Tom Roby introduced the down-up algebra $\mathcal A$. The algebra $\mathcal A$ is associative, noncommutative, and infinite-dimensional. It is defined by two generators $A,B$ and two relations called the down-up…
We compute symmetry algebras of a system of two equations y^(k)=z^(l)=0, where 2<=k<l. It appears that there are many ways to convert such system of ODEs to an exterior differential system. They lead to different series of…
We give a process to construct non-split, three-dimensional simple Lie algebras from involutions of sl(2,k), where k is a field of characteristic not two. Up to equivalence, non-split three-dimensional simple Lie algebras obtained in this…
A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…
The symmetry group structures of two dimensional coupled nonlinear Shr\"{o}dinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending…
We establish an explicit algebra isomorphism between the quantum reflection algebra for the $U_q(\hat{sl_2})$ R-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal…