Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Andrei Minchenko"'
Publikováno v:
Mathematics of Computation.
Algorithms working with linear algebraic groups often represent them via defining polynomial equations. One can always choose defining equations for an algebraic group to be of degree at most the degree of the group as an algebraic variety. However,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9314c818c6463b2a77c9501ed592ffa8
https://doi.org/10.1090/mcom/3695
https://doi.org/10.1090/mcom/3695
Autor:
Andrei Minchenko
Publikováno v:
Proceedings of the American Mathematical Society. 143:2317-2330
We consider central extensions $Z\hookrightarrow E\twoheadrightarrow G$ in the category of linear differential algebraic groups. We show that if $G$ is simple non-commutative and $Z$ is unipotent with the differential type smaller than that of $G$, t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6f18c9527b6d5441a958ddd88cf480b
https://doi.org/10.1090/s0002-9939-2015-12639-1
https://doi.org/10.1090/s0002-9939-2015-12639-1
Autor:
Alexey Ovchinnikov, Andrei Minchenko
For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard–Vessiot, and linearly differentially clos
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a9b2b035e68af482b6f091851d841ba
http://arxiv.org/abs/1707.08620
http://arxiv.org/abs/1707.08620
A complex vector space $V$ is an \'etale $G$-module if $G$ acts rationally on $V$ with a Zariski-open orbit and $\dim G=\dim V$. Such a module is called super-\'etale if the stabilizer of a point in the open orbit is trivial. Popov proved that reduct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::745f6fed057a32b43cf2b37a3f30e38c
http://arxiv.org/abs/1706.08735
http://arxiv.org/abs/1706.08735
Autor:
Alexey Ovchinnikov, Andrei Minchenko
Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently developed. Ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18cee5f8da54046102e3fdf1fd56393e
Autor:
Andrei Minchenko, E. B. Dynkin
Publikováno v:
Transformation Groups. 15:813-841
The root system Σ of a complex semisimple Lie algebra is uniquely determined by its basis (also called a simple root system). It is natural to ask whether all homomorphisms of root systems come from homomorphisms of their bases. Since the Dynkin dia
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::65955057917b694e615969a2d91bccb5
https://doi.org/10.1007/s00031-010-9100-y
https://doi.org/10.1007/s00031-010-9100-y
Publikováno v:
Mathematische Annalen
Mathematische Annalen, 2017, 368 (1-2), pp.587-632. ⟨10.1007/s00208-016-1442-x⟩
Mathematische Annalen, Springer Verlag, 2017, 368 (1-2), pp.587-632. ⟨10.1007/s00208-016-1442-x⟩
Mathematische Annalen, 2017, 368 (1-2), pp.587-632. ⟨10.1007/s00208-016-1442-x⟩
Mathematische Annalen, Springer Verlag, 2017, 368 (1-2), pp.587-632. ⟨10.1007/s00208-016-1442-x⟩
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the representation t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da210d61bb37418b84ae25debd79d509
http://arxiv.org/abs/1505.07068
http://arxiv.org/abs/1505.07068