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We generalize Atsuyama's result on the geometry of symmetric spaces of type EVI to the case of fields of characteristic zero. We relate the possible mutual positions of two points with the classification of balanced symplectic ternary algebras (also known as Freudenthal triple systems). [ABSTRACT FROM AUTHOR]

In this paper we study commutative algebraic monoid structures on affine spaces over an arbitrary field of characteristic zero. We obtain full classification of such structures on A K 2 and A K 3 and describe some generalizations on A K n for any dimension n. [ABSTRACT FROM AUTHOR]

We prove that frame set F g for imaginary shift of sinc-function g (t) = sin ⁡ π b (t − i w) t − i w , b , w ∈ R ∖ { 0 } can be described as F g = { (α , β) : α β ⩽ 1 , β ⩽ | b | }. In addition, we prove that F g = { (α , β) : α β ⩽ 1 } for window functions g of the form 1 t − i w (1 − ∑ k = 1 ∞ a k e 2 π i b k t) , such that ∑ k ⩾ 1 | a k | e 2 π | w b k | < 1 , w b k < 0. [ABSTRACT FROM AUTHOR]

We show that any adjoint absolutely simple linear algebraic group over a field of characteristic zero is the automorphism group of some projector on a central simple algebra. Projective homogeneous varieties can be described in these terms; in particular, we reproduce quadratic equations by Lichtenstein defining them. [ABSTRACT FROM AUTHOR]