相关论文: Constructing (almost) rigid rings and a UFD having…
A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are…
We estabilish some connections among the Makar-Limanov invariant, the Derksen invariant, and the existence of flexible points on an affine variety.
In this paper, we give an example of a finitely generated 3-dimensional C-algebra which has infinitely generated Derksen invariant as well as Makar-Limaonv invariant.
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…
Firstly we consider a finite dimensional Markov semigroup generated by Dunkl laplacian with drift terms. Using gradient bounds we show that for small coefficients this semigroup has an invariant measure. We then extend this analysis to an…
A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives…
We construct quasi-isometry invariants of a one-ended finitely presented group by considering the tree of cylinders of a two-ended JSJ decomposition of the group. When the group satisfies additional quasi-isometric rigidity hypotheses we…
The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…
We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant…
We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is…
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…
We investigate modified Makar-Limanov and Derksen invariants of an affine algebraic variety. The modified Makar-Limanov invariant is the intersection of kernels of all locally nilpotent derivations with slices and the modified Derksen…
We prove that certain volume preserving actions of Lie groups and their lattices do not preserve rigid geometric structures in the sense of Gromov. The actions considered are the "exotic" examples obtained by Katok and Lewis and the first…
A linear code with parameters of the form $[n, k, n-k+1]$ is referred to as an MDS (maximum distance separable) code. A linear code with parameters of the form $[n, k, n-k]$ is said to be almost MDS (i.e., almost maximum distance separable)…
A version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribbon *-categories which possess odd degenerate objects. This…
We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…
It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…
We describe the rings of invariants for the finite orthogonal groups of plus type in odd characteristic acting on the defining representations. We also describe the invariants of the corresponding Sylow subgroups in the defining…
We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results of Drinfeld for vector bundles.