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pro vyhledávání: '"Blok, Rieuwert"'
We classify all non-collapsing Curtis-Tits and Phan amalgams with $3$-spherical diagram over all fields. In particular, we show that amalgams with spherical diagram are unique, a result required by the classification of finite simple groups. We give
Externí odkaz:
http://arxiv.org/abs/1611.01038
Autor:
Blok, Rieuwert J., Hoffman, Corneliu G
In this note we establish the existence of all Curtis-Tits groups and Phan groups with $3$-spherical diagram as classified previously and investigate some of their geometric and group theoretic properties. Whereas it is known that orientable Curtis-T
Externí odkaz:
http://arxiv.org/abs/1611.00982
The classification of Curtis-Tits amalgams with {connected}, triangle free, simply-laced diagram over a field of size at least $4$ was completed in~\cite{BloHof2014b}. Orientable amalgams are those arising from applying the Curtis-Tits theorem to gro
Externí odkaz:
http://arxiv.org/abs/1511.06885
Publikováno v:
1-cohomology of simplicial amalgams of groups. R. J. Blok and C. G. Hoffman. J. Alg. Combin. 37(2013) no. 2:381-400
We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.
Externí odkaz:
http://arxiv.org/abs/1509.04679
Autor:
Blok, Rieuwert J., Gagola III, Stephen
In 1974 Orin Chein discovered a new family of Moufang loops which are now called Chein loops. Such a loop can be created from any group $W$ together with $\mathbb{Z}_2$ by a variation on a semi-direct product. We study these loops in the case where $
Externí odkaz:
http://arxiv.org/abs/1110.6390
Autor:
Blok, Rieuwert J., Carr, Benjamin
We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related to flips
Externí odkaz:
http://arxiv.org/abs/1012.2301
We prove that the Grassmannian of totally isotropic $k$-spaces of the polar space associated to the unitary group $\mathsf{SU}_{2n}(\mathbb{F})$ ($n\in \mathbb{N}$) has generating rank ${2n\choose k}$ when $\mathbb{F}\ne \mathbb{F}_4$. We also reprov
Externí odkaz:
http://arxiv.org/abs/1010.0205
In this short note, completing a sequence of studies by Cooperstein, Kasikova and Shult, we consider the k-Grassmannians of a number of polar geometries of finite rank n. We classify those subspaces that are isomorphic to the j-Grassmannian of a proj
Externí odkaz:
http://arxiv.org/abs/1010.0199
Using the construction of a nonorientable Curtis-Tits group of type $\tilde A_n$, we obtain new explicit families of expander graphs of valency five for unitary groups over finite fields.
Comment: Some results are strengthened
Comment: Some results are strengthened
Externí odkaz:
http://arxiv.org/abs/1009.0667
Autor:
Blok, Rieuwert J., Hoffman, Corneliu
Publikováno v:
Journal of Algebra 399 (2014) 978-1012
In a previous paper we define a Curtis-Tits group as a certain generalization of a Kac-Moody group. We distinguish between orientable and non-orientable Curtis-Tits groups and identify all orientable Curtis-Tits groups as Kac-Moody groups associated
Externí odkaz:
http://arxiv.org/abs/0911.0824