Related papers: Stability index for algebras with involution
This paper is concerned with the stability of deficiency indices of Hermitian subspaces (i.e., linear relations) under relatively bounded perturbations in Hilbert spaces. Several results about invariance of deficiency indices of Hermitian…
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve…
We equip the complex polynomial algebra C[t] with the involution which is the identity on C and sends t to -t. Answering a question raised by V.G. Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to…
The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what conditions a complex network of microscopic dynamical units…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
The asymptotic stability of several homological invariants of the graded pieces of a graded module has attracted quite a lot of attention over the last decades. We provide in this text several stability results together with estimates of…
We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a…
Using the momentum constraint, the standard evolution system is written in a fully first order form. The class of first order invariant algebraic slicing conditions is considered. The full set of characteristic fields is explicitly given.…
In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. The proof…
We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…
An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We…
We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The…
In this paper we extend To\"en's derived Hall algebra construction, in which he obtains unital associative algebras from certain stable model categories, to one in which such algebras are obtained from more general stable homotopy theories,…
Let $A$ be a commutative augmented ring and $I$ be its augmentation ideal. This paper shows that the sequence $\{I^n/I^{n+1}\}$ becomes stationary up to isomorphism. The result yields stability in the associated graded ring of $A$ along…
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…