Let A1 = K〈X,Y | [Y,X] = 1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(Y X) of A1 is Z. Let A1 → A1, X 7→ x, Y 7→ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of theWeyl algebra A1 is Z and the eigenvector algebra of ad(yx) is K〈x...

We generalize the notion of the rank-generating function of a graded poset. Namely, by enumerating different chains in a poset, we can assign a quasi-symmetric function to the poset. This map is a Hopf algebra homomorphism between the reduced incidence Hopf algebra of posets and the Hopf algebra of quasi-symmetric functions. This work implies that the zeta polynomial of a poset may be viewed in...

We compare the K-theory and K-homology of the well known CAR algebra. While the K0 group is infinitely generated, we show that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology group is very large. These results give some insight into the K-homology of AF-algebras. 1. The CAR algebra We...

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<abstract><p>The main purpose of this paper is to provide a full cohomology Hom-pre-Lie algebra with coefficients in given representation. This new type exploits strongly the Hom-type structure and fits perfectly simultaneous deformations multiplication homomorphism defining algebra. Moreover, we show that its second group classifies abelian extensions by representation.</p>&l...

For finitary set functors preserving inverse images several concepts of coalgebras A are proved to be equivalent: (i) A has a homomorphism into the initial algebra, (ii) A is recursive, i.e., A has a unique coalgebra-to-algebra morphism into any algebra, and (iii) A is parametrically recursive. And all these properties mean that the system described by A always halts in finitely many steps.

Patras, Reutenauer (J. Algebr. Comb. 16:301–314, 2002) describe a subalgebra A of the Malvenuto-Reutenauer algebra P . Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized v...

In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. Investigation supported by the Universi...

For finitary set functors preserving inverse images several concepts of coalgebras A are proved to be equivalent: (i) A has a homomorphism into the initial algebra, (ii) A is recursive, i.e., A has a unique coalgebra-to-algebra morphism into any algebra, and (iii) A is parametrically recursive. And all these properties mean that the system described by A always halts in finitely many steps.