Related papers: Ternary Virasoro - Witt Algebra
In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms.…
Do the Veronese rings of an algebra with straightening laws (ASL) still have an ASL structure? We give positive answers to this question in some particular cases, namely for the second Veronese algebra of Hibi rings and of discrete ASLs. We…
We explicitly demonstrate that the unitary representations of the $w_\infty$ algebra and its truncations are just the unitary representations of the Virasoro algebra.
We consider embeddings of the Virasoro algebra into other Virasoro algebras with different central charges. A Virasoro algebra with central charge c (assumed to be a positive integer) and zero mode operator L_0 can be embedded into another…
Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and…
We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We show that the Sugawara construction for the contracted affine algebra exists only for a fixed value of the level $k$, which is determined in terms of the dimension of…
The purpose of this paper is to study some Ternary color algebras. We generalize some results on ternary Leibniz algebras to the case of ternary Leibniz color algebras. In order to produce examples of ternary Leibniz color algebras from…
The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them, is obtained. Under…
We show that there is a braided tensor category structure on the category of $C_1$-cofinite modules for the (universal or simple) Virasoro vertex operator algebras of arbitrary central charge. In the generic case of central charge…
It is known that there are two inequivalent $\mathbb{Z}_2^2$-graded $osp(1|2)$ Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits two central elements, one is non-graded and the other is…
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
We focus on N = 3 chiral supergravity (SUGRA) which is the lowest N theory involving a spin-1/2 field, and derive the Ashtekar's canonical formulation of N = 3 SUGRA starting with the chiral Lagrangian constructed by closely following the…
It is shown that the $W_{1+\infty}$ algebra is nothing but the simplest subalgebra of a $q$-discretized \vi\ algebra, in the language of the KP hierarchy explicitly.
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that…
First, we give a new example of silting-discrete algebras. Second, one explores when the algebra of triangular matrices over a finite dimensional algebra is $\tau$-tilting finite. In particular, we classify algebras over which triangular…
This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear…
In the paper there are investigated various approximate representations of the infinite dimensional $\Bbb Z$--graded Lie algebras: the Witt algebra of all Laurent polynomial vector fields on a circle and its one-dimensional nontrivial…
We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott-Tomforde-Willis subshifts in terms of a…
n-ary algebras have played important roles in mathematics and mathematical physics. The purpose of this paper is to construct a deformation of Virasoro-Witt n-algebra based on an oscillator realization with two independent parameters (p, q)…