Related papers: Hilbert series for contractads and modular compact…
We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the…
The purpose of this paper is to study generalizations of Gamma-homology in the context of operads. Good homology theories are associated to operads under appropriate cofibrancy hypotheses, but this requirement is not satisfied by usual…
We propose an explicit relation between the cohomology of compactified and noncompactified moduli spaces of algebraic curves with punctures. This relationship generalizes one between commutative algebras and Lie algebras proposed by Lazard,…
Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra \(H\) using central idempotents in right coideal subalgebras and show that any…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…
We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…
We study the parameter space structure of degree $d \ge 3$ one complex variable polynomials as dynamical systems acting on $\C$. We introduce and study {\it straightening maps}. These maps are a natural higher degree generalization of the…
In this paper, we revisit the construction of the hairy graph complexes associated to a cyclic operad, by exploiting modules over the appropriate twisted linearization of the downward Brauer category (and working over a field of…
We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift of the usual functor of $R$-chains and the…
We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a…
We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$-dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of decades ago. We describe this operad by generators and…
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…
The symmetrization map $\pi:\mathbb C^2\rightarrow \mathbb C^2$ is defined by $ \pi(z_1,z_2)=(z_1+z_2,z_1z_2). $ The closed symmetrized bidisc $\Gamma$ is the symmetrization of the closed unit bidisc $\overline{\mathbb D^2}$, that is, \[…
We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of…
We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the…
The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of…
We use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating funtions), which count gauge invariant operators in N=1 supersymmetric SU(N_c), Sp(N_c), SO(N_c) and G_2 gauge theories with 1 adjoint…
We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex…
The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…
Let $\Lambda=kQ/I$ be a Koszul algebra over a field $k$, where $Q$ is a finite quiver. An algorithmic method for finding a minimal projective resolution $\mathbb{F}$ of the graded simple modules over $\Lambda$ is given in Green-Solberg.…