Related papers: The Friedlander-Milnor conjectures
We prove that Friedlander's generalized isomorphism conjecture on the cohomology of algebraic groups, and hence the Isomorphism Conjecture for the cohomology of the complex algebraic Lie group G(C) made discrete, are equivalent to the…
We prove the A-theoretic Farrell-Jones Conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
We have already conjectured 2 important guesses regarding Hypo-Lie algebra and modular simple Lie algebra. We would like to attach 2 important guesses more to this conjecture. Such new guesses are related to the Steinberg module.
We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for virtually solvable groups.
We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups.
These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).
In this paper, we focus on Oliver's $p$-group conjecture. We use elementary method to prove that Oliver's $p$-group conjecture holds for Sylow $p$-subgroups of unitary groups.
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
In this short note we confirm an analog of a conjecture of James Wiegold for finite dimensional nilpotent Lie algebras.
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.
The Langlands functoriality conjecture envisaged in the bisemialgebra framework is proved to correspond to the nonorthogonal completely reducible cuspidal representations of the bilinear algebraic semigroups.
We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.
We prove the K- and the $L$-theoretic Farrell-Jones conjecture with coefficients in additive categories and with finite wreath products for arbitrary lattices in virtually connected Lie groups.
We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…
In this paper, we give a proof of Vogan's fundamental parallelepiped (FPP) conjecture for complex simple Lie groups, resulting in a reduction step in the classification of irreducible unitary representations for these groups.
Recently, Moret\'o and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining…
We present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic…
We sketch several proofs of F\'ary--Milnor theorem.