The commutative Hopf monoid of set compositions is a fundamental internal to vector species, having undecorated bosonic Fock space the combinatorial algebra quasisymmetric functions. We construct geometric realization this over adjoint (essentialized) braid hyperplane arrangement, which identifies monomial basis with signed characteristic functions interiors permutohedral tangent cones. show th...

Abstract The automorphism group $\operatorname {Aut}(F_n)$ of the free $F_n$ acts on a space $A_d(n)$ Jacobi diagrams degree d n oriented arcs. We study -module structure by using two actions associated graded vector : an action general linear {GL}(n,\mathbb {Z})$ and Lie algebra $\mathrm {gr}(\operatorname {IA}(n))$ IA-automorphism {IA}(n)$ with its lower central series. extend to Andreadakis ...

Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. Its is shown that any sequence of Lie idempotents (one in each descent algebra) gives rise to a complete set of indecomposable orthogonal idempotents of each descent algebra, and various deformations of the classical sequence...

Over an Artin algebra Λ many standard concepts from homological algebra can be relativized with respect to a contravariantly finite subcategory C of mod-Λ, which contains the projective modules. The main aim of this article is to prove that the resulting relative homological dimensions of modules are preserved by stable equivalences between Artin algebras. As a corollary, we see that Auslander’...

In this paper we study the Hilbert space of analytic functions with finite Dirichlet integral in a connected open set C2 in the complex plane. We show that every such function can be represented as a quotient of two bounded analytic functions, each of which has a finite Dirichlet integral. This has several consequences for the structure of invariant subspaces of the algebra of multiplication op...

Let H denote a nite dimensional Hopf algebra with antipode S over a eld |. We give a new proof of the fact, due to Oberst and Schneider OS], that H is a symmetric algebra if and only if H is unimodular and S 2 is inner. If H is involutory and not semisimple, then the dimensions of all projective H-modules are shown to be divisible by char|. In the case where |is a splitting eld for H , we give ...

Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric space M to a t...

We generalize to universal algebra concepts originating from λ-calculus and programming to prove a new result on the lattice λT of λ-theories, and a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. In this paper we introduce the class of Church algebras (which includes all Boolean algebras, combinatory algebras, rings with unit a...

Let A = kG, the group algebra of some finite group where the characteristic of the field k divides |G|. In contrast to working over the complex field, the kGmodules are not usually semisimple. If a Sylow p-subgroup of G is not cyclic then there are infinitely many indecomposable kG-modules, and we usually enjoy little control over the category of such modules. It is therefore an important probl...