Related papers: On the relative opers in dimension one
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
The associative operad is a central structure in operad theory, defined on the linear span of the set of permutations. We build two analogs of the associative operad on the linear span of the set of packed words which turn out to be…
We study the holomorphic extendibility of $\text{Op}(p)u$, when $p$ is an analytic symbol, and explicit information is available on the domains of holomorphic extendibility of both $p$ and $u$. By a contour deformation argument, we obtain a…
A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of Lazarev et al., we construct an…
Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$ of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the Verdier's quotient category to get a relative derived category, where he localized…
In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in Ham(M), starting at the identity and ending on the subgroup that preserves a given Lagrangian…
We study different algebraic structures associated to an operad and their relations: to any operad $\mathbf{P}$ is attached a bialgebra,the monoid of characters of this bialgebra, the underlying pre-Lie algebra and its enveloping algebra;…
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…
We show that the positive zoom complexes, with fairly natural morphisms, form a dual category to the category of positive opetopes with contraction epimorphisms. We also show how this duality can be extended to opetopic cardinals.
We consider the graph whose vertex set is a conjugacy class ${\mathcal C}$ consisting of finite-rank self-adjoint operators on a complex Hilbert space $H$. The dimension of $H$ is assumed to be not less than $3$. In the case when operators…
In this paper we study certain families of motives, which arise as direct summands of the cohomology of the Dwork family. We computationally find examples of interesting families with the following three properties. Firstly, their geometric…
A difference operator on an associative algebra is an algebraic abstraction of the forward and backward difference operators. In this paper, we first introduce difference operators on associative $2$-algebras and consider the category of…
Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version…
In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations of the adele group under certain assumptions. We also give an application for classical holomorphic Hilbert-Siegel modular…
We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show…
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…
We study differential invariants of the third order linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles on two dimensional manifolds with respect to groups of…
We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local K\"ahler…
We explicitly construct an SO(2)-action on a skeletal version of the 2-dimensional framed bordism bicategory. By the 2-dimensional Cobordism Hypothesis for framed manifolds, we obtain an SO(2)-action on the core of fully-dualizable objects…