Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Petravchuk, A. P."'
Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and $\mathbb{K}[x,y]$ the polynomial ring. The group $\text{SL}_{2}\left(\mathbb{K}[x,y]\right)$ of all matrices with determinant equal to $1$ over $\mathbb{K}[x,y]$ can not be
Externí odkaz:
http://arxiv.org/abs/2412.03688
Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $\mathcal{M}(K)$ are called similar if $A_2=X^{-1}A_1X$ and $B_
Externí odkaz:
http://arxiv.org/abs/2408.04244
Let $\mathbb K$ be an algebraically closed field of characteristic zero, $\mathbb K[x, y]$ the polynonial ring in variables $x$, $y$ and let $W_2(\mathbb K)$ be the Lie algebra of all $\mathbb K$-derivations on $\mathbb K[x, y]$. A derivation $D \in
Externí odkaz:
http://arxiv.org/abs/2311.04866
Let $K$ be an algebraically closed field of characteristic zero, $A = K[x_1,\dots,x_n]$ the polynomial ring, $R = K(x_1,\dots,x_n)$ the field of rational functions, and let $W_n(K) = \Der_{K}A$ be the Lie algebra of all $K$-derivations on $A$. If $D
Externí odkaz:
http://arxiv.org/abs/2302.02441
We prove analogs of A.~Selberg's result for finitely generated subgroups of $\text{Aut}(A)$ and of Engel's theorem for subalgebras of $\text{Der}(A)$ for a finitely generated associative commutative algebra $A$ over an associative commutative ring. W
Externí odkaz:
http://arxiv.org/abs/2211.10781
Autor:
O.Ya. Kozachok, A.P. Petravchuk
Publikováno v:
Researches in Mathematics, Vol 32, Iss 1, Pp 93-100 (2024)
Let $\mathbb K$ be a field of characteristic zero, $A := \mathbb K[x_{1}, x_{2}]$ the polynomial ring and $W_2(\mathbb K)$ the Lie algebra of all $\mathbb K$-derivations on $A$. Every polynomial $f \in A$ defines a Jacobian derivation $D_f\in W_2(\ma
Externí odkaz:
https://doaj.org/article/8ea06d4779e9474299439fbf623ff1fa
Publikováno v:
In Linear Algebra and Its Applications 1 March 2025 708:150-158
Autor:
Bondarenko, Vitalij M., Futorny, Vyacheslav, Petravchuk, Anatolii P., Sergeichuk, Vladimir V.
Publikováno v:
Linear Algebra and its Applications 612 (2021) 188-205
I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) of commuting nilpotent operators on a vector space contains the problem of classifying an arbitrary t-tuple of linear operators. Moreover, it contains the probl
Externí odkaz:
http://arxiv.org/abs/2012.04038
Let $\mathbb K$ be a field of characteristic zero, $A$ an integral domain over $\mathbb K$ with the field of fractions $R = \text{Frac}(A),$ and $\text{Der}_{\mathbb{K}}A$ the Lie algebra of all $\mathbb K$-derivations on $A$. Let $W(A):=R\text{Der}_
Externí odkaz:
http://arxiv.org/abs/2002.10165
Autor:
Chapovskyi, Ie. Yu., Petravchuk, A. P.
Let $\mathbb K$ be an algebraically closed field of characteristic zero, $\mathbb K[X]$ the polynomial ring in $n$ variables. The vector space $T_n = \mathbb K[X]$ is a $\mathbb K[X]$-module with the action $x_i \cdot v = v_{x_i}'$ for $v \in T_n$. E
Externí odkaz:
http://arxiv.org/abs/1805.00933