Related papers: Negative K-groups of abelian categories

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial…

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

We characterise the virtually abelian groups which are fundamental groups of compact K\"ahler manifolds and of smooth projective varieties. We show that a virtually abelian group is K\"ahler if and only if it is projective. In particular,…

In this paper we give a complete description of the $h$-amalgamation bases in the class of non trivial abelian groups.

We show in this paper that a sub-critical pair $(A,B)$ of sufficiently "spread-out" Borel sets in a compact and second countable group $K$ with an \emph{abelian} identity component, must reduce to a Sturmian pair in either $\bT$ or $\bT…

We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…

We show that the automorphism group of the disk complex is isomorphic to the handlebody group. Using this, we prove that the outer automorphism group of the handlebody group is trivial.

The main result of the paper is that if $A$ is an abelian variety over a subfield $F$ of ${\bold C}$, and $A$ has purely multiplicative reduction at a discrete valuation of $F$, then the Hodge group of $A$ is semisimple. Further, we give…

We show that, under the definiteness of holomorphic sectional curvature, the spaces of some holomorphic tensor fields on compact Chern-K\"{a}hler-like Hermitian manifolds are trivial. These can be viewed as counterparts to Bochner's…

The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.

We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective…

Let G be a compact connected Lie group. We prove that the Fourier algebra A(G) is weakly amenable if and only if G is abelian.

For each prime $p$ and each positive integer $d$, we construct the first examples of second countable, topologically simple, $p$-adic Lie groups of dimension $d$ whose Lie algebras are abelian. This answers several questions of Gl\"ockner…

We resolve the Grothendieck-Serre question over an arbitrary base field $k$: for a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that every generically trivial $G$-torsor over $X$ trivializes Zariski semilocally on $X$.…

We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

If the group of a 2-knot group $K$ has an abelian normal subgroup of rank $\geq1$ which is not finitely generated then either $K$ has no minimal Seifert hypersurface or $K$ is topologically equivalent to Example 10 of Ralph Fox's``{\it A…

We prove that a countable group with an effective minimal non-elementary convergence group action is a Powers group. More strongly we prove that it is a strongly Powers group and thus its non-trivial subnormal subgroups are $C^*$-simple.

We show that holomorphic bundles on O(-k) for k > 0 are algebraic. We also show holomorphic bundles on O(-1) are trivial outside the zero section.

It is known that simple algebraic groups of type $F_4$ defined over a field $k$ are precisely the full automorphism groups of Albert algebras over $k$. We explore $R$-triviality for the group $\text{\bf Aut}(A)$ when $A$ is an Albert…