Related papers: Combinatorial Semigroup Bialgebras
Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule…
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…
We define and study the shuffle algebra $Sh_{m|n}$ of the quantum toroidal algebra $\mathcal E_{m|n}$ associated to Lie superalgebra $\mathfrak{gl}_{m|n}$. We show that $Sh_{m|n}$ contains a family of commutative subalgebras $\mathcal…
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…
The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative…
This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
We introduce strong group coalgebras, as a generalization of strongly graded coalgebras. We give several characterizations, and study two special types of strong group coalgebras, namely cleft group algebras (or crossed coproduct group…
Let $A$ and $B$ be two algebraic quantum groups (i.e. multiplier Hopf algebras with integrals). Assume that $B$ is a right $A$-module algebra and that $A$ is a left $B$-comodule coalgebra. If the action and coaction are matched, it is…
Using combinatorial properties of symmetric polynomials, we compute explicitly the Soergel modules for some permutations whose corresponding Schubert varieties are rationally smooth. We build from them diagram algebras whose module…
An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. In this paper, we study the cohomology of the complement of an abelian arrangement. For unimodular abelian…
In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called…
We study whether a unital associative algebra $ A $ over a field admits a decomposition of the form $A = Z(A) + [A,A]$ where $ Z(A) $ is the center of $ A $ and $ [A,A] $ denotes the additive subgroup of $A$ generated by all additive…
We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This generalization of the classical…
This is a study on pattern Hopf algebras in combinatorial structures. We introduce the notion of combinatorial presheaf, by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we consider…
We describe what might be called the "Hall-fusion" bialgebra constructed from a promonoidal double, and mention the corresponding face version for probicategories.
We present a new approach to Poincare duality for Cuntz-Pimsner algebras. We provide sufficient conditions under which Poincare self-duality for the coefficient algebra of a Hilbert bimodule lifts to Poincare self-duality for the associated…
Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie…
In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a…