On type-preserving representations of thrice punctured projective plane group

The Motivic Fundamental Group of the Punctured Projective Line

We describe a construction of an object associated to the fundamental group of P−{0, 1,∞} in the Bloch-Kriz category of mixed Tate motives. This description involves Massey products of Steinberg symbols in the motivic cohomology of the ground field.

Group of Homography in Real Projective Plane

Group Actions on Vector Bundles on the Projective Plane

We study the action of the group of automorphisms of the projective plane on the Maruyama scheme of sheaves MP 2(r, c1,c2) of rank r and Chern classes c1 = 0 and c2 = n and obtain sufficient conditions for unstability in the sense of Mumford’s geometric invariant theory. The conditions are in terms of the splitting behaviour of sheaves when restricted to lines in the projective plane. A very st...

Projective Group Representations in Quaternionic Hilbert Space

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi–centrality and centrality assumptions are also analyzed in generator terms, and implica...

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...