On the birational classification of algebraic group actions

2001 ◽  
Vol 65 (1) ◽  
pp. 57-70 ◽  
Author(s):  
Vsevolod E Kordonskii
Keyword(s):  
Algebraic Group ◽  
Group Actions

scholarly journals Invariants and separating morphisms for algebraic group actions

2015 ◽  
Vol 280 (1-2) ◽  
pp. 231-255 ◽  
Author(s):  
Emilie Dufresne ◽  
Hanspeter Kraft
Keyword(s):  
Algebraic Group ◽  
Group Actions

scholarly journals Spherical subgroups in simple algebraic groups

2015 ◽  
Vol 151 (7) ◽  
pp. 1288-1308
Author(s):  
Friedrich Knop ◽  
Gerhard Röhrle
Keyword(s):  
Algebraic Group ◽  
Closed Subgroup ◽  
Positive Characteristic ◽  
Dense Orbit ◽  
Simple Algebraic Group ◽  
Spherical Subgroup ◽  
Group A ◽  
General Deformation ◽  
Characteristic 2

Let $G$ be a simple algebraic group. A closed subgroup $H$ of $G$ is said to be spherical if it has a dense orbit on the flag variety $G/B$ of $G$. Reductive spherical subgroups of simple Lie groups were classified by Krämer in 1979. In 1997, Brundan showed that each example from Krämer’s list also gives rise to a spherical subgroup in the corresponding simple algebraic group in any positive characteristic. Nevertheless, up to now there has been no classification of all such instances in positive characteristic. The goal of this paper is to complete this classification. It turns out that there is only one additional instance (up to isogeny) in characteristic 2 which has no counterpart in Krämer’s classification. As one of our key tools, we prove a general deformation result for subgroup schemes that allows us to deduce the sphericality of subgroups in positive characteristic from the same property for subgroups in characteristic zero.

Odd Order Group Actions and Witt Classification of Innerproducts

1977 ◽  
Author(s):  
John P. Alexander ◽  
Pierre E. Conner ◽  
Gary C. Hamrick
Keyword(s):  
Group Actions ◽  
Order Group ◽  
Odd Order

Inequivalent, bordant group actions on a surface

1986 ◽  
Vol 99 (2) ◽  
pp. 233-238 ◽  
Author(s):  
Charles Livingston
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Group Actions ◽  
Free Actions ◽  
Orientable Surfaces

An action of a group, G, on a surface, F, consists of a homomorphismø: G → Homeo (F).We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with ø(g) orientation-preserving for all g ε G. In addition we will consider only effective (ø is injective) free actions. Free means that ø(g) is fixed-point-free for all g ε G, g ≠ 1. This paper addresses the classification of such actions.

scholarly journals Prevalência de ações táticas ofensivas de grupo no Campeonato Brasileiro de Futebol Série A (2018 e 2019)

2021 ◽  
Vol 19 (2) ◽  
pp. 1-5
Author(s):  
Allan Gabriel Silva Nascimento ◽  
João Marcelo Niquini Caríssimo ◽  
César Milagres Silva ◽  
Siomara Aparecida Silva
Keyword(s):  
Group Actions ◽  
Correlation Test

INTRODUÇÃO: O futebol é um dos esportes mais populares, sendo a tática um dos quesitos fundamentais para o sucesso. OBJETIVO: Identificar a associação entre os quantitativos das ações táticas ofensivas de grupo e os parâmetros de resultados das equipes mais bem colocadas no Campeonato Brasileiro Série A, temporadas 2018 e 2019.  MÉTODOS: Analisaram-se as seis equipes primeiras colocadas do Campeonato Brasileiro de Futebol Série A 2018 e 2019. O instrumento utilizado foi o Footstats. Foi realizada a análise descritiva das ações táticas ofensivas de grupo e a correlação de Spearman rho entre as variáveis das ações táticas com gols pró e pontos por meio do SPSS™ v. 23. RESULTADOS: A ação tática ofensiva de grupo “virada de bola” obteve associações significativas com “pontos” (r=0,829; p=0,042) e “gols pró” (r=0,943; p=0,005) no campeonato de 2018. No campeonato de 2019, as ações táticas ofensivas de grupo “assistências” e “cruzamentos” evidenciaram associação significativa com “pontos” (r=0,812; p=0,050 e r=0,928; p=0,008, respectivamente), “gols pró” com “virada de bola” (r=0,943; p=0,005) e “pontos” (r=0,812; p=0,050). CONCLUSÃO: As ações táticas ofensivas de grupo associaram-se com gols pró e pontos na classificação final das primeiras equipes em ambos os anos. Destaca-se a “virada de bola” no campeonato de 2018, além de “assistências” e “cruzamento” na edição de 2019, como ações que podem ser relevantes para a conquista dos pontos e por consequência melhores resultados dentro de tais competições.ABSTRACT. Prevalence of offensive tactical group actions in the Brazilian Football Championship A Series (2018-2019)BACKGROUND: Soccer is one of the most popular sports worldwide, with tactics being one of the fundamental requirements for teams to succeed in this sport. OBJECTIVE: o identify the association between the quantitative of the group’s offensive tactical actions and the parameters of result of the top six teams of the A-Series Brazilian Football Championship, seasons 2018 and 2019. METHODS: The top six teams of the two seasons were analyzed. The instrument employed was the software Footstats. Descriptive and correlation analyzes were carried out, together with Spearman rho correlation test between the variables of the group’s offensive tactical actions and the parameters of goals pro and points. RESULTS: The offensive tactical action “switch sides” obtained significant associations with “points” (r=0.829; p=0.042) and “goals for” (r=0.943; p=0.005) in the 2018 season. In 2019, the offensive tactical actions “assistances” and “crosses” evidenced significant associations with “points” (r=0.812; p=0.050 and r=0.928; p=0.008, respectively), as well as “goals for” with “switch sides” (R=0.943; p=0.005) and “points” (r=0.812; p=0.050). CONCLUSION: The number of groups offensive tactical actions were associated with the number of goals pro and points in the final classification of the top teams of both seasons. The actions “switch sides” in season 2018, besides “assistances” and “crosses” in season 2019 appeared as relevant for the achievements of points and, consequently, better results in such competitions.

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