By computing the completely bounded norm of flip map on Haagerup tensor product [Formula: see text] associated to a pair continuous mappings locally compact Hausdorff spaces text], we establish simple characterization Beck-Chevalley condition for base change operator modules over commutative text]-algebras, and descent theorem fields Hilbert spaces.

Relying on the classification of simple Lie algebras over algebraically closed fields characteristic >3, we show that any finite-dimensional central 5-graded algebra a field k ? 2 , 3 is Chevalley type, i.e. quotient algebraic -group. As consequence, prove all structurable and Kantor pairs arise from 5-gradings type.

Hecke algebras arise naturally in the representation theory of nite or p-adic Cheval-ley groups, as endomorphism algebras of certain induced representations (see Carter 9], Lusztig 42], and the references there). They may also be viewed as quotients of group algebras of Artin{Tits braid groups, and then they can be used to construct invariants of knots and links (Jones 34]). Another point of vi...

We prove that the $\mathbb{F}_p[[t]]$-standard Hausdorff spectrum of a compact $\mathbb{F}_p[[t]]$-analytic group contains real interval and it coincides with full unit when is soluble. Moreover, we show classical Chevalley groups over $\mathbb{F}_p[[t]]$ not full, since 1 an isolated point thereof.