17 citations · 63 across the 39 of their papers we have counts for
13 papers · 1 filter
Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology
Mikhail Borovoi
We develop a hypercohomology theory of a group with coefficients in a crossed module, and apply it to define abelianization maps for Galois cohomology of reductive algebraic groups…
Real non-degenerate two-step nilpotent Lie algebras of dimension eight
Mikhail Borovoi, Bogdan Adrian Dina, Willem A. de Graaf
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure…
A short proof of Timashev's theorem on the real component group of a real reductive group
Mikhail Borovoi, Ofer Gabber
Using results of Cartan, Matsumoto, and Casselman, we give a short proof of Timashev's theorem computing the real component group π_0 G(R) of a connected reductive real algebraic g…
Galois cohomology and component group of a real reductive group
Mikhail Borovoi, Dmitry A. Timashev
Let G be a connected reductive group over the field of real numbers R. Using results of our previous joint paper, we compute combinatorially the first Galois cohomology set H^1(R,G…
Quasi-connected reductive groups
Mikhail Borovoi, Andrei A. Gornitskii, Zev Rosengarten
We introduce the notion of a quasi-connected reductive group over an arbitrary field to be an almost direct product of a connected semisimple group and a quasi-torus (a smooth grou…
Galois cohomology of real semisimple groups via Kac labelings
Mikhail Borovoi, Dmitry A. Timashev
For a connected semisimple group G over the field of real numbers R, using a method of Onishchik and Vinberg, we compute the first Galois cohomology set H^1(R,G) in terms of Kac la…