Related papers: The Push the button algorithm for contragredient L…
One important example of a transposed Poisson algebra can be constructed by means of a commutative algebra and its derivation. This approach can be extended to superalgebras, that is, one can construct a transposed Poisson superalgebra…
In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients - the cuspidal parabolic subalgebras. We explicate also the maximal…
The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition to construct a colour Lie algebra from an $\epsilon$-orthogonal representation of an $\epsilon$-quadratic colour…
In this paper, we focus on how we can interpret the actions of the elements in the Gelfand spectrum of a weighted Fourier algebra on connected Lie groups. They can be viewed as evaluations on specific points of the complexification of the…
A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as…
We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a topological supercharge we construct an…
We study how to generate new Lie algebras $\mathcal{G}(N_0,..., N_p,...,N_n)$ from a given one $\mathcal{G}$. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter $\lambda$ which…
We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real…
We present a framework for the reduction of various geometric structures extending the classical coisotropic Poisson reduction. For this we introduce constraint manifolds and constraint vector bundles. A constraint Serre-Swan theorem is…
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…
For any cocommutative Hopf algebra $H$ and a left $H$-module $V$, we construct an operad $\mathcal{P}^{cl}_H(V)$, which in the special case when $H$ is the algebra of polynomials in one variable reduces to the classical operad…
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this…
We investigate the structure of ultrafilters on Boolean algebras in the framework of Tukey reducibility. In particular, this paper provides several techniques to construct ultrafilters which are not Tukey maximal. Furthermore, we connect…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
Extremal Graph Theory heavily relies on exploring bounds and inequalities between graph invariants, a task complicated by the rapid combinatorial explosion of graphs. Various tools have been developed to assist researchers in navigating…
An action for 3+1-dimensional supergravity genuinely invariant under the Poincare supergroup is proposed. The construction of the action is carried out considering a bosonic lagrangian invariant under both local Lorentz rotations and local…
In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an $S$-expansion process (with either resonance or $0_S$-resonant-reduction) for reaching a target Lie (super)algebra from a…
The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute…