Zobrazeno 1 - 10
of 250
pro vyhledávání: '"17B25"'
Autor:
Slovák, Jan, Souček, Vladimír
The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of all objects
Externí odkaz:
http://arxiv.org/abs/2409.01844
We classify up to isomorphism the gradings by arbitrary groups on the exceptional classical simple Lie superalgebras $G(3)$, $F(4)$ and $D(2,1;\alpha)$ over an algebraically closed field of characteristic $0$. To achieve this, we apply the recent met
Externí odkaz:
http://arxiv.org/abs/2408.06700
Autor:
De Medts, Tom, Meulewaeter, Jeroen
We study simple Lie algebras generated by extremal elements, over arbitrary fields of arbitrary characteristic. We show: (1) If the extremal geometry contains lines, then the Lie algebra admits a $5 \times 5$-grading that can be parametrized by a cub
Externí odkaz:
http://arxiv.org/abs/2407.10672
This document presents the solutions to the exercises in the book "Albert algebras over commutative rings" published by Cambridge University Press, 2024.
Comment: Approximately 300 pages
Comment: Approximately 300 pages
Externí odkaz:
http://arxiv.org/abs/2406.02933
Kac's ten-dimensional simple Jordan superalgebra over a field of characteristic 5 is obtained from a process of semisimplification, via tensor categories, from the exceptional simple Jordan algebra (or Albert algebra), together with a suitable order
Externí odkaz:
http://arxiv.org/abs/2404.01719
Publikováno v:
Reviews in Mathematical Physics 3 (2024) 2450027
We present a Veronese formulation of the octonionic and split-octonionic projective and hyperbolic planes. This formulation of the incidence planes highlights the relationship between the Veronese vectors and the rank-1 elements of the Albert algebra
Externí odkaz:
http://arxiv.org/abs/2311.11907
Autor:
Paul, Pampa
Let G be a connected simple Lie group with finite centre, K be a maximal compact subgroup of G, and rank(G)= rank(K). Let \frak{g}_0=Lie(G), \frak{k}_0=Lie(K) \subset \frak{g}_0, \frak{t}_0 be a maximal abelian subalgebra of \frak{k}_0, \frak{g}=\fra
Externí odkaz:
http://arxiv.org/abs/2309.11099
This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$, $\mathbb{
Externí odkaz:
http://arxiv.org/abs/2308.09052
Autor:
Dimitrov, Ivan, Fioresi, Rita
We generalize the notion of a root system by relaxing the conditions that ensure that it is invariant under reflections and study the resulting structures, which we call generalized root systems (GRSs for short). Since both Kostant root systems and r
Externí odkaz:
http://arxiv.org/abs/2308.06852
Autor:
Fontanals, Cristina Draper
A new highly symmetrical model of the compact Lie algebra $\mathfrak{g}^c_2$ is provided as a twisted ring group for the group $\mathbb{Z}_2^3$ and the ring $\mathbb{R}\oplus\mathbb{R}$. The model is self-contained and can be used without previous kn
Externí odkaz:
http://arxiv.org/abs/2307.12086