Related papers: Truncation of Unitary Operads
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…
We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3, and for primary ideals whose resolutions are linear except…
Using punctual gluing of $t$-structures, we construct an analogue of S. Morel's weight truncation functors (for certain weight profiles) in the setting of motivic sheaves. As an application we construct a canonical motivic analogue of the…
In this paper we study extensions of commuting tuples of symmetric and isometric operators to commuting tuples of self-adjoint and unitary operators. Some conditions which ensure the existence of such extensions are presented. A…
We survey the operator algebras arising as commutants modulo normed ideals of finite sets of hermitian operators and connections to perturbations of operators and noncommutative geometry.
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd…
Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…
We study the structure of the Gelfand-Tsetlin subalgebras of a family of idempotent truncations of the generalized blob algebras. We obtain optimal presentations in terms of generators and relations, monomial basis and dimension formula.
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…
We provide a superselection theory of symmetry defects in 2+1D symmetry enriched topological (SET) order in the infinite volume setting. For a finite symmetry group $G$ with a unitary on-site action, our formalism produces a $G$-crossed…
We study consistent truncations in the framework of Exceptional Generalised Geometry. We classify the 4-dimensional gauged supergravities that can be obtained as a consistent truncation of 10/11-dimensional supergravity. Any truncation is…
We introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces. In particular, we study the bilinear ideals $\mathcal{N}$ of completely nuclear, $\mathcal{I }$ of completely integral, $\mathcal{E}$…
Brown and Goodearl stated a conjecture that provides an explicit description of the topology of the spectra of quantum algebras. The conjecture takes on a more explicit form if there exist separating Ore sets for all incident pairs of torus…
We introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of non-uniformity. We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses…
We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula--plus a few other technical requirements. The…
We introduce a Gentzen-style framework, called layered sequent calculi, for modal logic K5 and its extensions KD5, K45, KD45, KB5, and S5 with the goal to investigate the uniform Lyndon interpolation property (ULIP), which implies both the…
We construct an analogue of the Livernet--Loday operad for two compatible brackets. The Livernet--Loday operad can be used to define $\star$-products and deformation quantization for Poisson structures. We make use of our operad in the same…
In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singulatities and…