Whitney algebras and Grassmann’s regressive products

Whitney algebras and Letterplace superalgebras

I’ll give an outline of the theory of Whitney algebras of a matroid, with the notions of geometric product and the excahnge relations, I’ll give the letterplace superalgebra coding of these algebras, and I’ll show how this coding allows to get the exchange relations directly from the superstraightening laws. I’ll not speak about the Lax Hopf algebra structure of Whitney algebras. All this is pa...

Baxter Algebras and Shuffle Products ∗

Vertex Algebras and the Class Algebras of Wreath Products

The Jucys-Murphy elements for wreath products Γn associated to any finite group Γ are introduced and they play an important role in our study on the connections between class algebras of Γn for all n and vertex algebras. We construct an action of (a variant of) the W1+∞ algebra acting irreducibly on the direct sum RΓ of the class algebras of Γn for all n in a group theoretic manner. We establis...

Quantum algebras and symplectic reflection algebras for wreath products

To a finite subgroup Γ of SL2(C), we associate a new family of quantum algebras which are related to symplectic reflection algebras for wreath products Sl o Γ via a functor of Schur-Weyl type. We explain that they are deformations of matrix algebras over rank-one symplectic reflection algebras for Γ and construct for them a PBW basis. When Γ is a cyclic group, we are able to give more informati...

Products in almost f-algebras

Let A be a uniformly complete almost f -algebra and a natural number p ∈ {3, 4, . . . }. Then Πp(A) = {a1 . . . ap; ak ∈ A, k = 1, . . . , p} is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σp(A) = {a; 0 ≤ a ∈ A} as positive cone.