Quadrangular Algebras. (MN-46)

Compact totally disconnected Moufang buildings

“…(A quadrangular algebra is defined in [44]; references to all the other relevant definitions can be found in [37, 16.1-16.9].) By [37, 38.9], we can assume that in Case Q D the indifferent set Ξ = (k, k 0 , L 0 ) is proper as defined in [37, 38.8].…”

The Kneser-Tits conjecture for groups with Tits-index $$ {\text{E}}_{8,2}^{66} $$ over an arbitrary field

“…Our main background reference for quadratic forms is [6], although we mostly use the notation of [23]. Let (K, L, q) be a quadratic space.…”

“…19. In §3, we give proofs of Theorems 1.1 and 1.2 based on results in [23] and [24]. In particular, the notion of a quadrangular algebra introduced in Chapters 12-13 of [22] and in [23] plays a central role in these proofs.…”

“…In §3, we give proofs of Theorems 1.1 and 1.2 based on results in [23] and [24]. In particular, the notion of a quadrangular algebra introduced in Chapters 12-13 of [22] and in [23] plays a central role in these proofs. In §4 we show how the R-triviality of PGO + (q) for q as in Theorem 1.1(ii) in characteristic 0 yields another proof of Theorem 1.2 in arbitrary characteristic.…”

The real quadrangle of type E 6

“…a generalized quadrangle. In an abstract building-theoretic setting, it is studied in [25], [28], [29] in detail (over arbitrary fields). It is our aim to describe a projective embedding (called a Veronese embedding) of this generalized quadrangle over the reals, which is similar in spirit to Freudenthal's description of the Cayley plane.…”