Related papers: The Friedlander-Milnor conjectures
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.
According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results…
We use the notion of the principal three-dimensional subgroup of a simple Lie group to identify certain special subspaces of the Lie algebra and address the question of whether these are calibrated for invariant forms on the group.
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.
In joint work with M. Hopkins and C. Teleman we find a new description of the Verlinde algebra associated to a compact Lie group. In this expository account we describe twisted K-theory, prove the theorem for the group SU(2), and motivate…
We consider several questions related to Pontryagin duality in the category of abelian pro-Lie groups.
Let F be a global field, A its ring of adeles, G a reductive group over F. We prove the Baum-Connes conjecture for the adelic group G(A).
In this paper, we completely classify three-dimensional Lorentzian $Ein(2)$ Lie groups.
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
We present a proof of Milnor conjecture in dimension 3 based on Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature bounded below. It is different from [Liu] that relies on minimal surface theory.
The purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one of the classical Brunn-Minkowski inequality in Euclidean space.
We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…
We present a simplified and more intuitive proof of a theorem of Peng and Xiao, which constructs a Lie algebra from any 2-periodic triangulated k-category (satisfying some finiteness assumptions).
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We explore to what extent the underlying variety of a connected algebraic group or the underlying manifold of a real Lie group determines its group structure.
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…
In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having an advantage over existing theories in that…
We prove a conjecture of Frenkel-Gaitsgory-Kazhdan-Vilonen on some exponential sums related to the geometric Langlands correspondence. Our main ingredients are the resolution of Lusztig scheme of lattices introduced by Laumon and the…