Zobrazeno 1 - 10
of 625
pro vyhledávání: '"14R20"'
Let $A$ be a retract of the polynomial ring in three variables over a field $k$. It is known that if ${\rm char}\: (k) = 0$ or ${\rm tr.deg}\:_k A \not= 2$ then $A$ is a polynomial ring. In this paper, we give some sufficient conditions for $A$ to be
Externí odkaz:
http://arxiv.org/abs/2412.13424
Autor:
Arzhantsev, Ivan
Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2412.10936
We complete the classification of algebraic monoids on the affine 3-space. The result is based on a reduction of the general case to the case of commutative monoids. We describe the structure of the set of idempotents and of the center of each monoid
Externí odkaz:
http://arxiv.org/abs/2412.09559
Autor:
Blanc, JérŔemy
We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group. In higher
Externí odkaz:
http://arxiv.org/abs/2411.17143
Autor:
Freudenburg, Gene
Working over a field $k$ of characteristic zero, we study the ring $\mathfrak{R}=\mathfrak{D}^{\mathbb{Z}_2}$ where $\mathfrak{D}=k[x_0,x_1,x_2]/(2x_0x_2-x_1^2-1)$ and $\mathbb{Z}_2$ acts by $x_i\to -x_i$. $\mathfrak{D}$ admits an algebraic $SL_2(k)$
Externí odkaz:
http://arxiv.org/abs/2411.15879
Autor:
Liendo, Alvaro, Petitjean, Charlie
In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface. These vari
Externí odkaz:
http://arxiv.org/abs/2411.14645
Autor:
Kikteva, Veronika
We obtain a criterion for the automorphism group of an affine toric variety to be connected in combinatorial terms and in terms of the divisor class group of the variety. The component group of the automorphism group of a non-degenerate affine toric
Externí odkaz:
http://arxiv.org/abs/2409.10349
Autor:
Kuroda, Shigeru
Let $X$ be an integral affine scheme of characteristic $p>0$, and $\sigma $ a non-identity automorphism of $X$. If $\sigma $ is $\textit{exponential}$, i.e., induced from a ${\bf G}_a$-action on $X$, then $\sigma $ is obviously of order $p$. It is ea
Externí odkaz:
http://arxiv.org/abs/2408.02204
Autor:
Lim, Lek-Heng, Ye, Ke
We show that the flag manifold $\operatorname{Flag}(k_1,\dots, k_p, \mathbb{R}^n)$, with Grassmannian the special case $p=1$, has an $\operatorname{SO}_n(\mathbb{R})$-equivariant embedding in an Euclidean space of dimension $(n-1)(n+2)/2$, two orders
Externí odkaz:
http://arxiv.org/abs/2407.12546
Autor:
Andrist, Rafael B.
We study the Lie algebra of polynomial vector fields on a smooth Danielewski surface of the form $x y = p(z)$ with $x,y,z \in \mathbb{C}$. We provide explicitly given generators to show that: 1. The Lie algebra of polynomial vector fields is generate
Externí odkaz:
http://arxiv.org/abs/2406.14702