Related papers: Spectral sequences of operad algebras
Some arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $n\ge2$ Euclidean BPS monopole is not defined over $\overline{\mathbb{Q}}$ if smooth.
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…
In this paper we discuss why the passage from simplicial algebras over a Cat operad to algebras over that operad involves apparently unavoidable technicalities.
The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
Using the description of enriched $\infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $\infty$-operads as certain modules in symmetric sequences. For $\mathbf{V}$ a symmetric monoidal model…
We introduce a framework for implementing quantum operations as steady states of a subsystem in an extended Hilbert space. Each operation has a spectral criterion for reaching the steady state. This adds a `spectral switch' mechanism to the…
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called…
An algebraic criterion, in terms of closure under power operations, is determined for the existence and uniqueness of generalized trun- cated Brown-Peterson spectra of height 2 as E_\infty-ring spectra. The criterion is checked for an…
We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2. In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain…
We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…
In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations…
Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.
In this note, we consider the Lyndon--Hochschild--Serre spectral sequence corresponding to the first Frobenius kernel of an algebraic group G, computing the extensions between simple $G$-modules. We state and discuss a conjecture that…
If X is a cosimplical $E_{n+1}$ space then Tot(X) is an $E_{n+1}$ space and its mod 2 homology $H_*(Tot(X))$ has Dyer-Lashof and Browder operations. It's natural to ask if the spectral sequence converging to $H_*(Tot(X))$ admits compatible…
A formula is given in terms of secondary characteristic classes for the leading order contribution to the spectral flow for a path of twisted Dirac operators on an odd dimensional, Riemannian manifold when the twisting is done by a path of…
We consider discontinuous operations of a group $G$ on a contractible $n$-dimensional manifold $X$. Let $E$ be a finite dimensional representation of $G$ over a field $k$ of characteristics 0. Let $\mathcal{E}$ be the sheaf on the quotient…
Necessary or sufficient conditions are presented for the existence of various types of actions of Lie groups and Lie algebras on manifolds.
Motivated by calculations of motivic homotopy groups, we give widely attained conditions under which operadic algebras and modules thereof are preserved under (co)localization functors