Related papers: Higher order peak algebras

Let $p$ be a prime. We complete the classification on pointed Hopf algebras of dimension $p^2$ over an algebraically closed field $k$. When $\text{char}k \neq p$, our result is the same as the well-known result for $\text{char}k=0$. When…

The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions. We give a new…

Let $\mathbb{k}$ be an algebraically closed field. We give a complete classification of non-connected pointed Hopf algebras of dimension $16$ with char$\,\mathbb{k}=2$ that are generated by group-like elements and skew-primitive elements.…

We construct finite-dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We…

Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…

We present an overview of the notions of exact sequences of Hopf algebras and tensor categories and their connections. We also present some examples illustrating their main features; these include simple fusion categories and a natural…

This article surveys results on graded algebras and their Hilbert series. We give simple constructions of finitely generated graded associative algebras $R$ with Hilbert series $H(R,t)$ very close to an arbitrary power series $a(t)$ with…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an…

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…

We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf…

Hopf algebroids are generalizations of Hopf algebras to less commutative settings. We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system into a Hopf algebroid without…

Nonlinear $sl(2)$ algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a general context. The linear $sl(2)$-case…

Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…

In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct…

We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the…

We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411--430.], and show that they can be obtained as homomorphic images of certain subalgebras of the…

We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two…

Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.

We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…