Zobrazeno 1 - 10
of 90
pro vyhledávání: '"SKIP GARIBALDI"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 11 (2023)
Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative nonassociative algebras and also arise naturally in the context of simple affine group schemes of type $\mathsf {F}_4$ , $\mathsf {E}_6$ , o
Externí odkaz:
https://doaj.org/article/8ab81ca7b5414cbe918fec5a199be2d1
Autor:
Maurice Chayet, Skip Garibaldi
Publikováno v:
Forum of Mathematics, Sigma, Vol 9 (2021)
We give a construction that takes a simple linear algebraic group G over a field and produces a commutative, unital, and simple non-associative algebra A over that field. Two attractions of this construction are that (1) when G has type $E_8$, the al
Externí odkaz:
https://doaj.org/article/ba270bbf4d9c4f519b6df0a7767f99bd
Autor:
SKIP GARIBALDI, ROBERT M. GURALNICK
Publikováno v:
Forum of Mathematics, Pi, Vol 3 (2015)
We study the problem of determining, for a polynomial function $f$ on a vector space $V$, the linear transformations $g$ of $V$ such that $f\circ g=f$. When $f$ is invariant under a simple algebraic group $G$ acting irreducibly on $V$, we note that t
Externí odkaz:
https://doaj.org/article/55e34f1cb850484091274bff40b1e887
Publikováno v:
PLoS ONE, Vol 10, Iss 2, p e0115730 (2015)
We analyze the spending of individuals in the United States on lottery tickets in an average month, as reported in surveys. We view these surveys as sampling from an unknown distribution, and we use non-parametric methods to compare properties of thi
Externí odkaz:
https://doaj.org/article/3c1dea7884a84bafa94dae06399babdd
Autor:
Benedict H. Gross, Skip Garibaldi
Publikováno v:
Indagationes Mathematicae. 32:987-1004
We study embeddings $J \rightarrow G$ of simple linear algebraic groups with the following property: the simple components of the $J$ module Lie($G$)/Lie($J$) are all minuscule representations of $J$. One family of examples occurs when the group $G$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::890fc22c37291c51ce584638f545164b
https://doi.org/10.1016/j.indag.2020.10.005
https://doi.org/10.1016/j.indag.2020.10.005
Autor:
Skip Garibaldi, Robert M. Guralnick
Publikováno v:
Michigan Mathematical Journal. 72
We prove a myriad of results related to the stabilizer in an algebraic group $G$ of a generic vector in a representation $V$ of $G$ over an algebraically closed field $k$. Our results are on the level of group schemes, which carries more information
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::abc8e25657296a91d891f9af86ce4967
https://doi.org/10.1307/mmj/20217216
https://doi.org/10.1307/mmj/20217216
Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise naturally in the context of simple affine group schemes of type $F_4$, $E_6$, or $E_7$. We study these o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2756fa93a02ce077cf22def58b78229
http://arxiv.org/abs/2205.09896
http://arxiv.org/abs/2205.09896
Autor:
Robert M. Guralnick, Skip Garibaldi
Publikováno v:
Transformation Groups. 25:819-841
In parts I and II, we determined which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::83f32696149185544b62e6ad7b2a4f84
https://doi.org/10.1007/s00031-020-09590-4
https://doi.org/10.1007/s00031-020-09590-4
Autor:
Skip Garibaldi, Robert M. Guralnick
Publikováno v:
Transformation Groups. 25:793-817
We determine which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero. This relies on bound
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4447580980be9105d39209ede511a406
https://doi.org/10.1007/s00031-020-09591-3
https://doi.org/10.1007/s00031-020-09591-3
Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the