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We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra…
Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
Collinear factorization and the leading-twist operator product expansion (OPE) in perturbative QCD express suitably inclusive observables in scale-separated kinematics as composites of perturbative short-distance coefficients with universal…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
Let g be a Lie algebra of type A,D,E with fixed Cartan subalgebra h, root system R and Weyl group W. We show that a choice of Coxeter element C gives a root basis for g. Moreover we show that this root basis gives a purely combinatorial…
This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…
For every finitary set functor F we demonstrate that free algebras carry a canonical partial order. In case F is bicontinuous, we prove that the cpo obtained as the conservative completion of the free algebra is the free completely…
The homology of free Lie algebras with coefficients in tensor products of the adjoint representation working over Q contains important information on the homological properties of polynomial outer functors on free groups. The latter…
Let V be a cofibrantly generated monoidal model category and let M be a monoidal V-model category. Given a cofibrant C-coloured operad P in V, we give sufficient conditions for the fibrant replacement and cofibrant replacement functors in…
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…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled planar trees extending the Loday-Ronco and…
Starting from any unital colored PROP $P$, we define a category $P(P)$ of shapes called $P$-propertopes. Presheaves on $P(P)$ are called $P$-propertopic sets. For $0 \leq n \leq \infty$ we define and study $n$-time categorified $P$-algebras…
We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $\mathcal{C}$ a braided tensor category, we give a detailed construction of the…
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with…
The aim of this paper is to establish a duality between the category of discrete groupoids and the category of geometrically transitive commutative Hopf algebroids in the sense of P. Deligne and A. Brugui\`eres. In one direction we have the…
We construct vertex operator representations for the full (N+1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl(N)…
Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and…