Results 41 to 50 of about 322,239 (148)

Local automorphisms of finite dimensional simple Lie algebras

, 2018
Let ${\mathfrak g}$ be a finite dimensional simple Lie algebra over an algebraically closed field $K$ of characteristic $0$. A linear map $\varphi:{\mathfrak g}\to {\mathfrak g}$ is called a local automorphism if for every $x$ in ${\mathfrak g}$ there is
Costantini, Mauro
core   +1 more source

Matrix rings and linear groups over a field of fractions of enveloping algebras and group rings, I

Journal of Algebra, 1984
The goal here is to show that the ring \(D_ n\) of \(n\times n\) matrices over the division ring of fractions D of a universal enveloping algebra enjoys properties similar to that of a PI-algebra over a field. Let H be a Lie algebra over the field K, let U(H) be its universal enveloping algebra and let D be the ring of fractions of U(H).
openaire   +2 more sources

Surjectivity of maps induced on matrices by polynomials and entire functions

, 2016
We determine a necessary and sufficient condition for a polynomial over an algebraically closed field $k$ to induce a surjective map on matrix algebras $M_n(k)$ for $n \ge 2$.
Mondal, Shubhodip
core   +1 more source

Space of linear differential operators on the real line as a module over the Lie algebra of vector fields

, 1996
Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To define this family, one considers arguments of differential operators as tensor-densities of degree $ $.) In this ...
Gargoubi, H., Ovsienko, V. Yu.
openaire   +3 more sources

Reflection Groups and Differential Forms

, 2007
We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms.
Hartmann, Julia, Shepler, Anne V.
core   +2 more sources

Koszul hypersurfaces over the exterior algebras [PDF]

, 2014
We prove that if $E$ is an exterior algebra over a field, $h$ is a quadratic form, then $E/(h)$ is Koszul if and only if $h$ is a product of two linear forms.Comment: 4 ...
Nguyen, Hop D.
core  

How To Use Neural Networks To Investigate Quantum Many-Body Physics

PRX Quantum, 2021
Over the past few years, machine learning has emerged as a powerful computational tool to tackle complex problems in a broad range of scientific disciplines.
Juan Carrasquilla, Giacomo Torlai
doaj   +1 more source

Automorphism groups of some non-nilpotent Leibniz algebras

Researches in Mathematics
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[a,[b,c]]=[[a,b],c]+[b,[a,c]]$ for all $a,b,c\in L$. A linear transformation $f$ of $L$
L.A. Kurdachenko, P.Ye. Minaiev, O.O. Pypka   +2 more
doaj   +1 more source

On the determination of the Singer transfer

Vietnam Journal of Science, Technology and Engineering, 2018
Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] with the degree of each generator xi being 1, where F2 denote the prime field of two elements, and let GLk be the general linear group over F2 which acts regularly on Pk.
Sum Nguyen
doaj   +1 more source

An analog of the Hille theorem for hypercomplex functions in a finite-dimensional commutative algebra

Математичні Студії
We prove that a locally bounded and differentiable in the sense of Gâteaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorc and it is a monogenic function.
S. A. Plaksa, V. S. Shpakivskyi, M. V. Tkachuk   +2 more
doaj   +1 more source