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pro vyhledávání: '"Lubkov, Roman"'
Autor:
Lubkov, Roman, Nekrasov, Ilia
We establish two characterizations of an algebraic group scheme $\bigwedge^m GL_n$ over $\mathbb{Z}$. Geometrically, the scheme $\bigwedge^m GL_n$ is a stabilizer of an explicitly given invariant form or, generally, an invariant ideal of forms. Algeb
Externí odkaz:
http://arxiv.org/abs/2310.00101
Autor:
Lubkov, Roman
We initiate the study of subgroups $H$ of the general linear group $GL_{\binom{n}{m}}(R)$ over a commutative ring $R$ that contain the $m$-th exterior power of an elementary group $\bigwedge^mE_n(R)$. Each such group $H$ corresponds to a uniquely def
Externí odkaz:
http://arxiv.org/abs/2203.13683
Autor:
Lubkov, Roman, Nekrasov, Ilia
We prove a first part of the standard description of groups $H$ lying between an exterior power of an elementary group $\bigwedge^m E_n(R)$ and a general linear group $GL_{n \choose m}(R)$ for a commutative ring $R$, $2\in R^*$ and $n\geqslant 3m$. T
Externí odkaz:
http://arxiv.org/abs/2201.13034
Autor:
Lubkov, Roman
For the second fundamental representation of the general linear group over a commutative ring $R$ we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary matrix and
Externí odkaz:
http://arxiv.org/abs/2102.05010
Autor:
Lubkov, Roman, Nekrasov, Ilia
We present several explicit systems of equations defining exterior square of the general linear group as an affine group scheme. Algebraic ingredients of the equations, exterior numbers, are translated into the language of weight diagrams correspondi
Externí odkaz:
http://arxiv.org/abs/1803.05721
Autor:
Lubkov, Roman, Nekrasov, Ilia
In the present paper, we prove the first part in the standard description of groups $H$ lying between $m$-th exterior power of elementary group $E(n,R)$ and the general linear group $GL_{\binom{n}{m}}(R)$. We study structure of the exterior power of
Externí odkaz:
http://arxiv.org/abs/1801.07918
Autor:
Lubkov, Roman, Nekrasov, Ilia
Publikováno v:
Linear & Multilinear Algebra; Mar2024, Vol. 72 Issue 4, p563-584, 22p