Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties. 1 A precise version of the localization theorem Let X be a topological space with...

Let H be a cocommutative weak Hopf algebra and let (B,φB) left H-module algebra. In this paper, for twisted convolution invertible morphism σ:H2→B we define its obstruction θσ as Sweedler 3-cocycle with values in the center of B. We obtain that class vanish third cohomology group HφZ(B)3(H,Z(B)) if, only there exists 2-cocycle α:H2→B such H⊗B can endowed crossed product structure α keeping coho...

For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capre...

We briefly review and illustrate our procedure to ‘decouple’ by transformation of generators: either a Hopf algebra H from a Hmodule algebra A1 in their cross-product A1>⊳H; or two (or more) H-module algebras A1,A2. These transformations are based on the existence of an algebra map A1>⊳H → A1. Preprint 02-64 Dip. Matematica e Applicazioni, Università di Napoli DSF/29-2002 ∗Contribution to the P...

Let T be the Itô Hopf algebra over an associativa algebra L into which the universal enveloping algebra U of the commutator Lie algebra L is embedded as the subalgebra of symmetric tensors. We show that there is a one-to-one correspondence between deformations ∆[h] of the coproduct in T and pairs ( → d [h], ← d [h]) of right and left differential maps which are deformations of the differential ...

Let H be a finite dimensional Hopf C*-algebra, H1 Hopf*-subalgebra of H. This paper focuses on the observable algebra AH1 determined by in nonequilibrium spin models, which there is copy each lattice site, and ? link, where denotes dual Furthermore, using iterated twisted tensor product +*-algebras, one can prove that algebraAH1 *-isomorphic to C*-inductive limit ... o .

In this paper, we construct explicitly a NCS system ([Z4]) Ω T ∈ (H GL) ×5 over the Grossman-Larson Hopf algebra H GL ([GL] and [F]) of rooted trees labeled by elements of a nonempty W ⊆ N of positive integers. By the universal property of the NCS system (NSym,Π) formed by the generating functions of certain NCSF’s ([GKLLRT]), we obtain a graded Hopf algebra homomorphism TW : NSym → H GL such t...

In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension A H to each twisted algebra H obtained from a Hopf algebra H by twisting its product with the help of a cocycle α. The algebra A H is a flat deformation of H over a “big” central subalgebra B H and can be viewed as the noncommutative analogue of a versal torsor in the sense of Serre. After surveying the results...