Related papers: Presentations for Globular Operads
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
We develop Lie theory in the category $\text{Ver}_4^+$ over a field of characteristic 2, the simplest tensor category which is not Frobenius exact, as a continuation of arXiv:2406.10201. We provide a conceptual proof that an operadic Lie…
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set…
We build on the methods introduced by Friedmann, Hanlon, Stanley, and Wachs, and further developed by Brauner and Friedmann, to construct additional classes of presentations of Specht modules. We obtain these presentations by defining a…
Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
This paper attempts to provide a more or less self-contained introduction into theory of the Grothendieck-Teichmueller group and Drinfeld associators using the theory of operads and graph complexes.
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher…
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number…
We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
This note describes an application of the theory of generalised Burnside rings to algebraic representation theory. Tables of marks are given explicitly for the groups $S_4$ and $S_5$ which are of particular interest in the context of…
In this paper we address the problem of constructing a class of representations of Clifford algebras that can be named "alphabetic (re)presentations". The Clifford algebras generators are expressed as m-letter words written with a…
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced.
In this article we present a detailed study of the existing constructions of colilimits in the category of symmetrical operations. In addition, some examples of operads obtained from colimits of other operads are presented.
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal…
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…
We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We shall concern only the quotient singularity of hypersurface type. The abelian group $A_r(n)$ for $A$-type…