Zobrazeno 1 - 10
of 178
pro vyhledávání: '"de Graaf, Willem"'
The theory of nilpotent orbits of simple Lie algebras has seen tremendous developments over the past decades. In this context an important role is played by the component group of the stabilizer of a nilpotent element. In this work, the aim is to sho
Externí odkaz:
http://arxiv.org/abs/2407.11801
Autor:
Dietrich, Heiko, de Graaf, Willem A.
We present a computational approach to determine the space of almost-inner derivations of a finite dimensional Lie algebra given by a structure constant table. We also present an example of a Lie algebra for which the quotient algebra of the almost-i
Externí odkaz:
http://arxiv.org/abs/2403.05905
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure constants for these real Lie algebras.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2308.11413
Autor:
Borovoi, Mikhail, de Graaf, Willem A.
Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles in G. Mor
Externí odkaz:
http://arxiv.org/abs/2308.04962
In this paper we classify the orbits of the group SL(3,F)^3 on the space F^3\otimes F^3\otimes F^3 for F=C and F=R. This is known as the classification of complex and real 3-qutrit states. We also give an overview of physical theories where these cla
Externí odkaz:
http://arxiv.org/abs/2305.01270
Autor:
de Graaf, Willem A.
Publikováno v:
Contemp. Math., 783, 27--46, 2023
We illustrate the Lie theoretic capabilities of the computational algebra system GAP4 by reporting on results on nilpotent orbits of simple Lie algebras that have been obtained using computations in that system. Concerning reachable elements in simpl
Externí odkaz:
http://arxiv.org/abs/2303.15927
Autor:
de Graaf, Willem, Lê, Hông Vân
Publikováno v:
Linear Algebra and its Applications Volume 703 , 15 December 2024, Pages 423-445
We consider the semisimple orbits of a Vinberg $\theta$-representation. First we take the complex numbers as base field. By a case by case analysis we show a technical result stating the equality of two sets of hyperplanes, one corresponding to the r
Externí odkaz:
http://arxiv.org/abs/2212.03775
We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-virtually abelian discontinuous group actions on homogen
Externí odkaz:
http://arxiv.org/abs/2206.01069
We classify states of four rebits, that is, we classify the orbits of the group $\widehat{G}(\mathbb R) = \mathrm{\mathop{SL}}(2,\mathbb R)^4$ in the space $(\mathbb R^2)^{\otimes 4}$. This is the real analogon of the well-known SLOCC operations in q
Externí odkaz:
http://arxiv.org/abs/2201.11777