Related papers: Compatible associative products and trees
We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
The method of direct computation of universal (fibred) product in the category of commutative associative algebras of finite type with unity over a field is given and proven. The field of coefficients is not supposed to be algebraically…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we…
In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In…
As an instance of a linear action of a Hopf algebra on a free associative algebra, we consider finite group gradings of a free algebra induced by gradings on the space spanned by the free generators. The homogeneous component corresponding…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
For any set S, the free magmatic algebra spanned by card(S) binary products is the vector space spanned by the set of all planar rooted binary trees with the internal nodes colored by the elements of S, graded by the number of leaves of a…
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov…
Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a…
We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…
We show that the infinite symmetric product of a connected graded-commutative algebra over the rationals is naturally isomorphic to the free graded-commutative algebra on the positive degree subspace of the original algebra. In particular,…
We present amalgamated free products satisfying coupling rigidity with respect to the automorphism group of the associated Bass-Serre tree. As an application, we obtain orbit equivalence rigidity for amalgamated free products of mapping…
In "Hopf algebra of the planar binary trees", Adv. Math. 139 (1998), no. 2, 293--309, we constructed by induction a graded associative product on the vector space generated by the planar binary trees (resp. the permutations). In the present…
We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of…
We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…
Supplementary results obtained after the completion of our previous paper are given together with discussing some examples. A quick review of the previous paper is also included.
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…
We compute the graded automorphisms of the upper triangular matrices, viewed as associative, Lie and Jordan algebras. We compute also the so called self-equivalences and Weyl and diagonal groups for every grading.