Related papers: Tauvel's height formula for quantum nilpotent alge…
This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.
For the quantum algebra U_q(gl(n+1)) in its reduction on the subalgebra U_q(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Z_q(gl(n+1),gl(n)) is given in terms of the generators and their defining relations.…
The main emphasis will be on height upper bounds in the algebraic torus G^{n}_{m}. By height we will mean the absolute logarithmic Weil height. Section 3.2 contains a precise definition of this and other more general height functions. The…
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit…
In this paper, we determine upper bound for the non-abelian tensor product of finite dimensional Lie superalgebra. More precisely, if $L$ is a non-abelian nilpotent Lie superalgebra of dimension $(k \mid l)$ and its derived subalgebra has…
For the Becchi-Rouet-Stora-Tyutin (BRST) invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the…
Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…
In this short note we confirm an analog of a conjecture of James Wiegold for finite dimensional nilpotent Lie algebras.
In this paper, we investigate nilpotent Lie algebras $ L $ of nilpotency class $3 $ and provide a complete classification of those satisfying $ \dim L^2 = 3 $ and $Z(L) = L^3 \cong A(2). $ Furthermore, we explicitly characterize the…
Let $G_q$ be the $q$-deformation of a simply connected simple compact Lie group $G$ of type $A$, $C$ or $D$ and $\mathcal{O}_q(G)$ be the algebra of regular functions on $G_q$. In this article, we prove that the Gelfand-Kirillov dimension…
In this paper, we systematically investigate the nilpotentizer and nilpotent graph for a Lie superalgebra over the field of characteristic not equal to 2. First, we establish some fundamental properties of the nilpotentizer. Next, we show…
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra…
An explicit form of the generators of quantum and ordinary semisimple algebras for an arbitrary finite-dimensional representation is found. The generators corresponding to the simple roots are obtained in terms of a solution of a system of…
In this article, we study properties as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the underlying graph. We show that graded simplicity and simplicity…
We generalize the results of [KMST] concerning equivariant quantization by means of Verma modules $M(\lambda)$ for generic weight $\lambda$ to the case of general $\lambda$. We consider the relationship between the Shapovalov form on an…
Coulomb branches of a set of $3d\ \mathcal{N}=4$ supersymmetric gauge theories are closures of nilpotent orbits of the algebra $\mathfrak{so}(n)$. From the point of view of string theory, these quantum field theories can be understood as…
For an arbitrary countable field, we construct an associative algebra that is graded, generated by finitely many degree-1 elements, is Jacobson radical, is not nil, is prime, is not PI, and has Gelfand-Kirillov dimension two. This refutes a…
We introduce two constructions to obtain left-invariant Ricci-flat pseudo-Riemannian metrics on nilpotent Lie groups, one based on gradings, the other on filtrations, both depending on the combinatorics of the set of weights. As an…
It is proved that that every nilpotent contraction in a quotient C*-algebra can be lifted to a nilpotent contraction. As a consequence we get that the universal C*-algebra generated by a nilpotent contraction is projective. This answers the…
Let $\mathfrak{g}$ be a simple complex Lie algebra.A generalized Verma module induced from a one-dimensional representation of a parabolic subalgebra of $\mathfrak{g}$ is called a scalar generalized Verma module of $\mathfrak{g}$. In this…