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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]

Abstract Let G be a split semisimple linear algebraic group over a field k 0. Let E be a G -torsor over a field extension k of k 0. Let h be an algebraic oriented cohomology theory in the sense of Levine–Morel. Consider a twisted form E / B of the variety of Borel subgroups G / B over k. Following the Kostant–Kumar results on equivariant cohomology of flag varieties we establish an isomorphism between the Grothendieck groups of the h-motivic subcategory generated by E / B and the category of finitely generated projective modules of certain Hecke-type algebra H which depends on the root datum of G , on the torsor E and on the formal group law of the theory h. In particular, taking h to be the Chow groups with finite coefficients F p and E to be a generic G -torsor we prove that all finitely generated projective indecomposable submodules of an affine nil-Hecke algebra H of G with coefficients in F p are isomorphic to each other and correspond to the (non-graded) generalized Rost–Voevodsky motive for (G , p). [ABSTRACT FROM AUTHOR]

We give an explicit construction of Lie algebras of type E 7 out of a Lie algebra of type D 6 with some restrictions. Up to odd degree extensions, every Lie algebra of type E 7 arises this way. For Lie algebras that admit a 56-dimensional representation we provide a more symmetric construction based on an observation of Manivel; the input is seven quaternion algebras subject to some relations. [ABSTRACT FROM AUTHOR]

Abstract: TGF-β1 induces differentiation and total inhibition of cardiac MyoFb cell division and DNA synthesis. These effects of TGF-β1 are irreversible. Inhibition of MyoFb proliferation is accompanied with the expression of Smad1, Mad1, p15Ink4B and total inhibition of telomerase activity. Surprisingly, TGF-β1-activated MyoFbs are growth-arrested not only at G1-phase but also at S-phase of the cell cycle. Staining with TUNEL indicates that these cells carry DNA damages. However, the absolute majority of MyoFbs are non-apoptotic cells as established with two apoptosis-specific methods, flow cytometry and caspase-dependent cleavage of cytokeratin 18. Expression in MyoFbs of proliferative cell nuclear antigen even in the absence of serum confirms that these MyoFbs perform repair of DNA damages. These results suggest that TGF-β1-activated MyoFbs can be growth-arrested by two checkpoints, the G1/S checkpoint, which prevents cells from entering S-phase and the intra-S checkpoint, which is activated by encountering DNA damage during the S phase or by unrepaired damage that escapes the G1/S checkpoint. Despite carrying of the DNA damages TGF-β1-activated MyoFbs are highly functional cells producing lysyl oxidase and contracting the collagen matrix. [Copyright &y& Elsevier]

We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of special orthogonal and spin groups. Besides, we apply these results to study Morava motivic decompositions of orthogonal Grassmannians. For instance, we determine all indecomposable summands of the Morava motives of a generic quadric. [ABSTRACT FROM AUTHOR]